Why do we "complete the square"?

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The quadratic formula is really useful, but its derivation is confusing to many. Like what is the point of "completing the square" anyway? In this video, I show how "completing the square" has a geometric interpretation--you are actually making the areas of two squares equal to each other!
Blog post (text/image summary): wp.me/p6aMk-4kG
You can read more about the history of the quadratic formula and its geometric roots from Cornell Mathematics professor David W. Henderson: www.math.cornel...
While researching this post, I came across a website that offers a visual interpretation of the quadratic formula that helped me design the graphics: sites.google.c...
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28 сен 2024

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Комментарии : 1,7 тыс.

@MindYourDecisions 4 года назад

This is also worth checking out: "New" Way To Solve Quadratic Equations That Everyone Is Talking About : ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-oWFRU-ula-A.html Professor Po-Shen Loh devised a different way to solve quadratic equations that could be helpful to many students.

@swagbhai1511 4 года назад

No bro factor method is so good and if he not work quadratic formula always worke

@Elly5955 4 года назад

You're so good in math, thank you for the explanation.

@TheOofster123 3 года назад

X^2 +2X+1 = (X+1)^2

@dskinner6263 2 года назад

The "couple of steps" you skipped in the second half of the video is what I came here to understand. It's been a long time since I studied math, and even my arithmetic is rusty when it comes to subtraction of fractions that include variables. Can you please point me to where I can learn why (-c/a)+(b²/4a²) = (b²-4ac)/(4a²), step by step? I remember it has to do with cross-multiplication, but I'm not getting it. :-(

@ccbgaming6994 2 года назад

You just multiply the term to make both have a common denominator, so here it would be by 4a

@mandolinic 8 лет назад

I've been using that formula for over 40 years and until now I've never wondered where it came from. Thanks for the enlightenment.

@DaveScottAggie 8 лет назад

Yes. 38 years for me. While the (negative lengths) kind of throw a wrench in, overall seeing it as matching up equal areas makes it easier to grasp.

@ghanshamchandel1854 8 лет назад

i used it for about 2 years and i knew it a year ago!

@hugofontes5708 8 лет назад

half way through an engineering major and didn't have a clue until now, I just used it until I got used to it

@michaelkarnerfors9545 7 лет назад

28 years here... and I am completely mind-blown. So amazingly intuitive!

@DerToasti 6 лет назад

the way it's usually derived is pretty simple though.

@nakamakai5553 6 лет назад

At the time (1973), I thought my 8th grade Advanced Math and my 9th grade Algebra teachers did a fabulous job of presenting the quadratic. I'm willing to concede that this is better. Very well done. 5 stars.

@Frances3654 8 лет назад

This video should be presented in every high school and middle school algebra class.

@billstokes9645 8 лет назад

+Benny Doe I agree, I do hope students share this with one another. I taught high school math years ago, I never made this as clear as the video does in less than ten minutes! Bravo.

@dragonite7780 8 лет назад

+Bill Stokes I thought I'd just tell my maths teacher, so that when he teaches gcse he can show this to his students so they can hopefully understand it better and not think 'its magic' or similar things.

@Peter_1986 8 лет назад

This is how math should be taught. I see too many math teachers who just present formulas out of nowhere without actually deriving them and explaining them, and this is pretty much like giving an instruction booklet to a beginner and ask him/her to use that booklet for everything. Yes, there are situations when certain topics might be useful and important but also too complicated to actually derive at that point, but if something *can* be derived without too much trouble then it *should* be derived. One rule of thumb is that students should be able to reprove those formulas to themselves with absolutely no extra help or reminders - everything should come from logical step-by-step reasonings.

@gregoryharlston3989 8 лет назад

As a new math teacher, I'll definitely be using this.

@hustler3of4culture3 8 лет назад

+alejandro cartes you can also tell your teacher that this is the same ancient method that Al-khwarismi used in around 820 ad in his compilation of algebra techniques. this geometric method has been around for millennia.

@AlpieInternet 5 лет назад

Everyone made fun of me using completing the square in 12th grade, whilst they were using the quadratic formula - they said I was wasting my time. I believed it was a lot more elegant. So I decided to prove to them that it was the same thing during one of my classes near the end of the year... took me forever - but I eventually got it. IF ONLY I knew this. SUCH an elegant proof - great video explaining it!

@yashuppot3214 5 лет назад

Yeah more elegant but y consume more time

@sunjidasultana4648 6 месяцев назад

I prefer factorization more than the formula or the completing square method

@philj9594 3 месяца назад

@@sunjidasultana4648 Well I mean, most good teachers will show you that all three methods are best depending on the numbers you are working with. Basically you go through and see if it can easily solved with factorization/completing the square. If the answer to both is they can't (too tedious/"not nice" numbers), you just go straight to the quadratic formula.

@PrimalPower 6 дней назад

@@sunjidasultana4648 Factorization doesn't work for all quadratics though

@DemonLordOfGluttony 3 дня назад

@@sunjidasultana4648 Factorization is mainly situational. It doesn't work when x,a,b,or c are surds or extremely large numbers

@damiannagel963 5 лет назад

Ok this is awesome. I've read on school books that the proof of the quadratic formula was too hard, but this is very simple and ties in with the concept of completing the squares. And you can even show it with pictures, for people that easily loses track of numbers.

@gregoryharlston3989 8 лет назад

I was struggling to teach some of my students the quadratic formula and I started thinking about it in similar terms such as this (minus the part about negative lengths). I knew some of my students might find this confusing. However, I took a chance and tried explaining the quadratic formula to my students in this way. For several of my students, I could see light bulbs going off--they got it! However, for many of my students, this only confused them further. I like your video. You explained it much better than I think I did (the colorful virtual manipulatives you used are extremely useful), so I think I'll be showing my students this in the future. I am a new math teacher and I try so hard to teach my students an intuitive way to think about math, like this for example. But sometimes, it seems that I only confuse them more. Also, if you've never been taught to think about math intuitively, then thinking intuitively requires a different orientation--kind of an undoing of just memorizing stuff to get answers. Keep up the great, great work!

@eric_enter9141 10 месяцев назад

Legend. Hope you had 7 good years since you commented this.

@tramothithanh2429 9 месяцев назад

vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_b%E1%BA%ADc_hai

@PatrickCraig-lh5is 4 месяца назад

Another piece of this is relevance to students' lives. Sure, "real world" applications utilizing the quadratic equation are everywhere, but in most cases students will counter with, "Yeah but I won't be using this in my own life, so why learn it?" For example: lobbing a basketball and modeling its motion with a quadratic might seem an ideal motivator, but how often do you see LeBron James out on the court with paper and pencil calculating the ball's trajectory? My own solution to this was to create a 2-D basketball simulator in the Scratch programming environment; players input a "best guess" angle and initial velocity and watched the results. This can springboard into a discussion of the math behind why the ball did or didn't go into the basket. We need to really put our backs into the relevance aspect of math. It's important.

@AgentMidnight 9 лет назад

I can think of a lot of people who could've benefited from this means of demonstration; much more straightforward and powerful than just forcing them to memorize the quadratic formula.

@AngieMyst 9 лет назад

We were taught this visual method to explain the formula in Algebra 2, but I don't think a lot of people made the connection or preferred to think in terms of numbers instead. I like this method the most.

@Minecraftster148790 9 лет назад

I find that u just remember it and then it is impossible to forget it

@dekippiesip 8 лет назад

+AngieMyst I knew about the algebraic derivation, but didn't connect it to anything geometrically. While geometry is much more intuitive in most cases, I think we can learn a lot from the ancient Greeks when it comes to this, as they connected nearly all mathematics to geometry.

@ydela1961 8 лет назад

+Cubik What kind of math teacher does that? In school all of my math teachers always gave the full explanations of all formulas we learned. We were not forced to remember the explanations as for the test only the formula was required. Most of my classmates memorized only the formulas, but I assure you, we had always the complete explanations. For me, memorizing a formula with no logic was a greater effort than remembering the (logic) way to get there. In a lot of cases because of poor memory, I did not remember formulas for the exam and I had to reconstruct them. That was easier for me that way. I was always in the 3 best students of my class in math... never knowing the formulas, always able to reconstruct them. So I guess in your class, with your teachers, I'd been in the 3 worst math student.

@AgentMidnight 8 лет назад

ydela1961 Congrats, I guess

@zetharic1610 7 лет назад

he made me understand it in 10 mins what 2 years in my school couldn't

@guitarraccoon1541 6 лет назад

But if you don't understand it then you haven't learned it, which goes against the very idea of schools.

@dirktween244 4 года назад

How about 30s ?

@Xanduur 7 лет назад

I am so glad I watched the proof at the end. Holy Cow! NOW I understand the HOW and WHY.

@putteyu29 7 лет назад

same här dude, :))) I had this quadratic completing thing a years ago, now i am really understanding it

@marknudelman1122 7 лет назад

Joe Edwards Same Mind Blow

@raycotter9558 7 лет назад

I all ways knew that the -B formula (the formula you showed at the end) came from factorising/simplifying ax^2+bx+c but I never could do this by myself ,my school never thought us the visual method I find this extremely helpful thank you

@Petrhrabal 8 лет назад

I am giving you the biggest like I have ever given on RU-vid!!! Thank you for enlightening one great frustration from an elementary school.

@elyseemutha8956 6 лет назад

Petrhrabal

@yoelbeche6213 9 месяцев назад

Very clear and precise teaching. This is by far the best explanation of completing the square method to solve quadratics on YT. Thanks brother!! ❤

@OscarBravoUSA 7 лет назад

Interesting and amazing. And I had to memorize deriving the quadratic formula the hard way. Thank you, sir.

@karineaudet6270 2 года назад

Good as akways but i asleep

@agt.yizint7217 Год назад

this kind of video may be helpful for those who interested in maths and always seek for the truth . textbook from school only gives us the equation straightforwardly but never show the proving steps so most of student could just understand how to use the equation to solve question but never understand how does the equation came from

@mattalexander4156 7 лет назад

I have a degree in math and use the quadratic formula ALL THE TIME when tutoring in Algebra... I have NEVER visualized it like this but instead used a song tune to get it stuck in students heads (to the tune of a jack in the box). I was extremely happy to see this though and will DEFINITELY be using this from now on when I explain it!!!!

@jd-gw4gr Год назад

i'm a math teacher of junior high school teaching an honor's math class, presh makes my job easier with excellent videos like this, presh; i thank you; the math community thanks you and most of all my students thank you.

@djalon95 8 лет назад

This was an amazing video! For the first time, I really understand the real meaning of the quadratic formula. Thanks

@doseoffaiyaz 7 месяцев назад

This is the best video on 'completing the square' on all of internet both graphically and algebraically.

@jmparchem Год назад

I remember showing my son who just learned completing the square how to derive the quadratic equation at the kitchen table. I got more and more excited as I progressed. My son and daughter just looked at me like I was crazy.

@userBBB 5 лет назад

4:55 the mystery length of -4

@francistan4674 5 лет назад

Negative quantities have physical meaning. Think negative displacement, negative velocity and acceleration. Going further, even "imaginary numbers" have real meaning in the physical world.

@stevezelaznik5872 4 года назад

Imagine the trajectory of a cannonball. The quadratic formula tells you the positive answer, when it will hit the ground, and the negative answer, when and where in the past it was shot out of the cannon.

@dirktween244 4 года назад

What is a box with a side of -4 ?? -4 is not wrong ! The use of the equation, IS wrong ! As noted by others, it could mean: Before your determined start time !

@nepasdisponible 3 года назад

@@francistan4674 But this is completely different from what you've told. This one deals with negative length.

@asr2009 Год назад

@@francistan4674 yes. but length or distance is a scalar quantity so cant be represented by negative numbers. this is why separation of algebra and geometry is important.

@chungkwanming 7 лет назад

That's awesome to have a graphical representation of completing the square. I learnt the algebraic way to solve quadratic equation in my high school but never have thought this could be done using geometry. I wonder if this method also works on solving cubic equation.

@thomasbassil140 2 года назад

It does, i forgot how but i've seen it done

@solarfluxman8810 6 лет назад

Presh Talwalkar - Very well done. I'm retired, and with teachers like you on RU-vid, I can learn faster than greased lightning.

@miguelsantos2572 9 лет назад

This video blew my mind. I always wanted to know where the formula comes from, and know I got it! Love your videos :)

@paulg687 5 лет назад

What this video clearly demonstrates, is what I've been saying for years and years. Generally, mathematics isn't difficult - well at this level. It's more the fact that you've been taught something that you commit to memory instead of understanding it. So, you see, it's not that you're bad at it - more like the education system and the way it's taught is useless. Once you understand something, as opposed to just memorizing it, it makes problem solving using this knowledge much easier.

@angelmendez-rivera351 5 лет назад

Paul G68 Actually, none of what you said demonstrates mathematics is not difficult. Yes, mathematics is taught very poorly, but so is every single subject in school. Also, homeschoolers generally agree that mathematics is still a more difficult subject than other subjects. So while education contributes to its difficulty, it is not the cause. Mathematics is difficult because it is by its very nature counterintuitive. Humans are not logical beings. Mathematics is based on understanding definitions, axioms, and using logical arguments and consistency, all things which humans are bad at. Humans have historically always used their emotions to think, never actual logic. Everyone has logically inconsistent beliefs for this reason. History does not behave like a formal logic system, and neither do arts or culture. Those are things we adapt to. Math behaves like a formal logic system because it is one by definition, and as such, it resides outside the first nature and second nature to humans. For the record, geometric visualizations aren't any more intuitive than algebraic ones. Plenty of students struggle with those too. The only reason it looks like there aren't any is because students who struggle with them are always accomodated for by the education system, since curriculums are almost always purely algebraic visualization. But in reality, geometric visualizations don't make intuitive, it only makes it somewhat more accessible to students. Math is not intuitive. The vast majority of mathematics simply cannot be learned by visualizations like these, and the vast majority of mathematics isn't intuitive. These are an outlier and can be explained visually only because, in the grand scheme of things, it's one of the easiest subjects in mathematics. It's literally the second easiest thing after arithmetic. That's why they teach it after arithmetic.

@paulg687 5 лет назад

Angel Mendez-Rivera : well you have your opinion and I disagree. Maths is taught in a way that makes it difficult. Want an example. Add up in your head, like you were taught as school these numbers. 1467+1667. Remember do it in your head. What you’ll find is, you’ll struggle because of the way you were taught. Now watch this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-hesKQ_y1P7k.html So, you see after you watch this video it’s much easier and intuitive. Theres the demonstration of what I was saying. So once again, I respectfully disagree with what you are saying. Once you build up a basic understanding of maths, it’s a case of building on top of that to further your learning. Nothing hard in that.

@americanswan 7 лет назад

this is the best explanation of this concept I've ever seen.

@williamhuang8309 Год назад

So the quadratic formula is just compressing all the steps of completing the square into one equation.

@pssilva3973 3 года назад

That is the best demostration of the quadratic formula I've ever seen.

@soberTrezviy 2 года назад

another nice visualisation is that -b/2a turns out to be a coordinate x of the parabola's top and |sqrt(D)/2a| = half-distance between roots of the equasion. it can be easily found by the substitution x'=x+b/2a . ax^2 + bx + c = a [ (x')^2 - b^2/4a + c/a] = 0 can be easily solved: (x')^2 = b^2/4a - c/a, => x' = ± sqrt(D)/2a, therefore x=x'-b/2a = -b/2a ± sqrt(D)/2a

@ace_stealth251ace9 9 лет назад

Thanks lot now I understand much more about it and how it actually works! Thanks love it!

@danielfoust6310 5 лет назад

Excellent explanation and I think necessary for all the visual learners like myself.

@VangelVe 3 года назад

A very good job. But you can take it a step further by showing that (-b/2a) is a line of symmetry for the parabola. That allows you to show that geometrically that the square root term divided by 2a is just a distance that you find the roots from that line of symmetry. It also allows kids to look at a quadratic function and find the vertex without the need to complete the square and encourages them to do more things in their head and to engage with problems rather than just follow formulas. It moves them towards greater understanding, which is what your great video does, rather than just memorizing and applying formulae.

@igorvieira344 8 лет назад

you should do it for the cubic and quartic equations formula

@Woodside235 8 лет назад

Hour and then a day long video, respectively.

@uhbayhue 8 лет назад

lol

@zelda12346 8 лет назад

And then explain the proof as to why there is no analytic formula for degree 5 or more.

@marek.p 6 лет назад

xapoliz vieira "complete the cube" and "complete the tesseract"? :P

@user-nm4ni5us8j 6 лет назад

x^3-6x^2=0 x^3-6x^2+12x-8=12x-8 (x-2)^3=12x-8 You have to add a x-term in the right side and because that it does not "works like a magic" with cubes.

@onafehts Год назад

That here is the most satisfying video I've seen in a very long while!

@angeldavidstarrmauas1934 4 года назад

I understood everything. I just wish you hadn't skipped those steps at the end... i wanted the whole thing to be crystal clear, no question marks. Thank you anyway for 90% of it. I will look up the rest.

@DANIELDALLAS_MATHs 4 года назад

For all steps with no question marks you might watch this ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Ot_SB6nrW8U.html It might work for U

@joaoleitaum2595 5 лет назад

Thank you! I spend so many years trying to find out where did it came from and you just made it! Now, my is life better!

@GDPlainA 3 года назад

Well, I'm not gonna ruin your time, but other than completing the square, you can just calculate the quadratic formula backwards.

@LuskyMJ 2 года назад

8:47 Can someone explain this step please? I figured it out. if anyone reads this in the future then here's the explanation: To make this easier to type out in RU-vid format I'm going to call the term b^2-4ac: "v1" and the term 4a^2: "v2". 1. We start by moving the b/2a term from the left side over to the right side: x = - b/2a +- sqrt(v1/v2) 2. Since we have a fraction inside the sqrt on the right side we can simplify it according to the rule: sqrt(a/b) = sqrt(a)/sqrt(b): x = - b/2a +- sqrt(v1)/sqrt(v2) 3. We now have two fractions on the right side. To combine the two fractions into one they have to have the same denominator. Luckily for us they already have because the sqrt(v2) (4a^2) is equal to 2a. The equation now looks like this: x = - b/2a +- sqrt(v1)/2a 4. We can now combine the two fractions since they have the same denominator and we have the final equation (v1 is still equal to b^2-4ac): x = (-b +- sqrt(v1)) / ( 2a )

@gamerdude7800 11 месяцев назад

W , you are on the same level as the guy who asks 'music?' and gets a reply, except that u do it yourself 🗿🍷

@CZghost 8 лет назад

Wow, that's something our teacher never said to us :) Time to impress him :D

@PatrickCraig-lh5is 4 месяца назад

Overall a fantastic video; what I appreciated most was the derivation of the quadratic formula using completing the square. I often wonder why students are asked to solve quadratic equations via completing the square when that process, as applied to the general quadratic form, yields the quadratic formula. In the past I've given a single, high point value extra credit question on exams: _show me how to get the quadratic formula._ I would tell students in advance that it might be on there. Students really liked those points of course (major damage repair if they'd had a rough time on the rest of the exam), and even if they forget about the process in the future, they'll never quite be able to say, "that danged formula was a total mystery."

@dilipk.bhattacharyya1136 6 лет назад

I had done the derivation of the quadritic formula and also used the method of completing square . I wondered why it is called completing the square. Thanks for explanation

@dolevronen243 6 лет назад

My class is just learning about quadeadic equations, I'll show them your awesome explanation

@pranavkumars.4070 7 лет назад

The video was very intuitive. But can you please explain the geometrical meaning of negative value of x

@barfyman-362 7 лет назад

Pranav Kumar S. I think of X times X as adding X number of X spaces I think of -X times -X as removing X spaces of -X. basically like if there was some object taking up space, you are removing this "negative space". in other words multiplying positive numbers is like adding another room to you house, while multiplying negatives is like clearing out a full room so you have more space. either way, both give you more space.

@angelmendez-rivera351 5 лет назад

There is no geometrical meaning to having negative side lengths. There is a reason negative numbers are almost never used in geometry.

@lunaros4209 5 лет назад

Method 4: Dividing by a, setting p:= b/a and q:=c/a and applying x^2+px+q x = -p/2 (+-) sqrt(p^2/4 - q)

@ilafya 6 лет назад

Al-Khwarizmi's popularizing treatise on algebra (The Compendious Book on Calculation by Completion and Balancing, ca. 813-833 CE[7]:171) presented the first systematic solution of linear and quadratic equations. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications.[6]:14 Because he was the first to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation), he has been described as the father[8][9][10] or founder[11][12] of algebra. The term algebra itself comes from the title of his book (specifically the word al-jabr meaning "completion" or "rejoining").

@talan651 6 лет назад

I actually knew where it came from, but you make it way too easy!

@AliskaBierman 7 лет назад

So, so, so, so helpful! Thank you!!

@ProplusoneOrtiz 4 года назад

Wow, man. You open my eyes, your job is amazing!

@mil1lon 7 лет назад

Presh, that was fantastic. Apparently I had very poor teachers. You are the best! Thanks for taking something so a mathematical relationship I memorized and making it fun. Much appreciated.

@zad1737 7 лет назад

We just learned completing the square today so this is perfect! Thx sooo much!

@evelinavalentinova5002 2 года назад

x²+2x-15=0 x²+2x=15 Now we add a term that is given by the following formula: (b/2)² (2/2)²=1 By the way we need to have a=1, if not then divide both sides of the equation by "a" end then do this process. x²+2x+1=16 If you did this correctly you will always be able to factor this out like this: (a+b)², in this case :(x+1)² (x+1)²=16 Let's take the root on both sides: ✓(x+1)²=✓16 Now when we have this situation ✓y² , this is equal to |y| To understand this let's see an example: If we have y=2 then ✓2²=✓4=2 And if we have y=-2 ✓(-2)²=✓4=2 We always end up with the positive number, the absolute value of y, |y| . So ✓y²=|y| |x+1|=4 This means x+1=4, or x+1=-4 Because |-4|=4 So we have x1=3 and x2=-5 ax²+bx+c=0 4a(ax²+bx+c)=4a.0 4a²x²+4abx+4ac=0 4a²x²+4abx+4ac+b²=b² 4a²x²+4abx+b²=b²-4ac (2ax+b)²=b²-4ac 2ax+b=+-√b²-4ac 2ax=-b+-√b²-4ac x=(-b+-√b²-4ac)/2a This is how you can prove the formula

@JamesBath-is-here 7 лет назад

Outstanding explanation of completing the square! I finally get it.

@electricity2703 6 лет назад

This is the beauty of math

@sayhamshourav 3 года назад

Wow that's totally out of the world. you are such a genius.

@mahisamant2281 5 лет назад

THIS IS THE BEST THING IVE EVER SEEN OMG GOD BLESS YOU

@jintzie1950jth 5 лет назад

Great video! Best clarification of completing the square that I’ve seen.

@muppet005 3 года назад

What about a visual example in which the signs are different so that two rectangles must equal a negative area?

@toir1465 5 лет назад

I though that I will just need to answer “3” when I was looking at the thumbnail cuz 3^2 + 2*3 = 15

@chellurivenkatasatyanaraya240 3 года назад

Very nice reply but you are a learner of fundamental mathematics or master of mathematics or teacher of mathematics immaterial,we are all in one family we want to need support each other because we want to create a good human society.:-CHVSN as a INDIAN mathematician till I am a learner of fundamental mathematics.

@samibereket8097 Год назад

Excellent explanation!! It makes sense for first time.

@khn.majid1212 2 года назад

Learning and teaching mathematics it my hobby. Now I can explain it to my students 👍🏻👍🏻

@SaeedAcronia 7 лет назад

This method was first introduced by Al-khwarizmi, the father of Algebra, near 1000 years ago! could you believe that?!

@Argdut1106 6 лет назад

No.. this was given by Indian mathematician Sridhar Acharya even before that. It's his formula :)

@dyer308 6 лет назад

@@Argdut1106 Even before him, The Babylonians knew about this lol, But Al-Khwarizmi can be called the true father of the Quadratic equation since he was the first to put it in modern notation, combing its geometric/algebraic interpretations, exploring range and methods of obtaining all solutions, as well as applying it to finance and trade

@ubaidshah1910 5 лет назад

Arghya Dutta The person youre talking about is ayrabhatta, and no even he didnt invent algebra, it was known at babylonian times. Stop crediting everything to india

@ambrishabhijatya7842 5 лет назад

@@ubaidshah1910 Have you even read Al Khawarizmi ? Every single one of his books explicitly credit previous Indian mathematicians and that too in the title rather than in the footnotes.

@debgupta1 5 лет назад

@@ubaidshah1910 You are too innocent.He is talking about SHRIDHAR ACHARYA not ARYABHATT. Both were different.

@retanizer8263 5 лет назад

So basically I understand this than my actual Math teacher? **THANKS RU-vid RECOMMENDATION**

@sorry6726 5 лет назад

Wow i always wanted to know that. But too lazy to search online. Kudos to u👌🙏

@SkillslliK 5 лет назад

Mind = Blown! This was the only video about quadratic equation natural proof. Thank you man

@BKNeifert Год назад

The hardest thing to learn about the Quadratic Formula for me, was to factor in the area. Once I learned that, by playing with the shape of a chess board, x^2+2x+1 (which equals -1), I actually figured out you needed to make the equation equal to 64 for the problem to work. Which then the answer is 7. I rewatched this, and it made a whole lot more sense now, with that in mind. I've watched this video maybe half a dozen times. But, Presh, this is a reason why P cannot equal NP. Not every NP can be made into a polynomial. Just like you'd have to reduce a circle into quanta to make it into a square, you cannot take all NP difficulty equations and make them P. But, you can solve them like a Geometric proof, by reducing the more difficult NP geometry and finding it by different principles of mathematics and geometry. Which is how they solved a problem here just recently, I just can't remember which one. I was watching it on another channel about that. I was so close! Lol. I literally discovered it at the exact same time they did. I figured it out independently, but it was neat to see my concept was already being used.

@hotdogskid 8 лет назад

"im going to skip a few steps here..." Stop. Wait a minute. Fill my cup, put some explanation in it. So a magically jumps to the top and and is multiplied by 4?

@ongshenghao8827 8 лет назад

-c/a becomes 4a(-c)/4a(a) to get a common denominator of 4a^2

@hotdogskid 8 лет назад

oh that makes more sense

@gerald02121 8 лет назад

+Ong Sheng Hao He still should have taken 10 seconds to show that, would have made the video a lot more complete.

@benjamingoldstein14 6 лет назад

He doesn’t need to show you guys how to add fractions

@marklowery863 5 лет назад

Lame Bruno mars reference

@caigner 7 лет назад

Brilliant! I honestly can say I have never seen this explanation before. Now I know where the quadratic formula comes from. Thanks!

@gredangeo 6 лет назад

I don't think I was ever taught about 'completing the square'. I only saw the formula as it was presented, nothing more.

@GDPlainA 3 года назад

Another way to understand the quadratic formula is to go backwards. x=(-b+-sqrt(b^(2)-4ac)/2a 2ax=-b+-sqrt(b^(2)-4ac) 2ax+b=+-sqrt(b^(2)-4ac) (2ax+b)^2=b^(2)-4ac 4a^(2)x^(2)+4abx+b^(2)=b^(2)-4ac 4a^(2)x^(2)+4abx=-4ac ax^(2)+bx=-c ax^(2)+bx+c=0

@PuzzleAdda 4 года назад

Math, it's a puzzle to me. I love figuring out puzzles #PuzzleAdda

@deepakrajamurugesan1633 3 года назад

I still remember this method.. My maths teacher taught me this method but only few of us understood this method..

@TheDigiWorld Год назад

I really used to think that completing the square is just playing with x^2 + ax = b in a way to write it as (x + p)^2 = q and that's it... I did not have any idea there is such nice bit of geometry behind it.

@atiqurrahman8730 6 лет назад

Thanks. Your videos sooth my soul. I can feel numbers or the equations.

@rajaniramansrivastava8322 5 лет назад

Sir you should make more videos on all difficult topics so that we can understand it very clearly

@adityadwivedi2190 6 лет назад

Actually every 9th grade student knows it

@hamiltonianpathondodecahed5236 5 лет назад

Haan bhai .Our India is great

@Heisenberg9752 5 лет назад

Our country created lot's of things but invaders destroyed everything that's why we don't have enough proof... By the way we're still better in this

@mathfullyexplained 3 года назад

Try my channel mathfullyexplained. Many units

@zigaudrey 7 лет назад

I first thought of using the delta 1:02 but I forget thoses method, especially the second. 0:52 8:01 And that's explain the delta formula... I wanted to find it by going from the polynome of 2nd to the Delta Formula in order to understand it!

@vincentkingsdale8334 8 месяцев назад

7:49 be great if you didn't skip those steps

@confused6526 7 лет назад

Awesome explanation of what the formula means. Thanks

@liber8r 2 года назад

When geometry intersects with algebra, good things happen. Thanks!

@afaqabas 6 лет назад

Really great video, i didn't think much of it at the beginning but the end was amazing.

@angeldude101 Год назад

My class covered completing the square, but it was communicated entirely as a mechanical algebraic transformation; no geometry whatsoever. Compared to that, the quadratic formula, while still largely out of nowhere, was much easier to remember if for no other reason than the video we were down of someone _singing_ it.

@marshallcheung2731 5 месяцев назад

I wish I knew this decades ago. Thanks!

@rotterdamstudio320 7 лет назад

Fantastic, great insight. I could derive that, but now it actually makes perfect sense.

@patilott6863 4 года назад

I may have to watch this a few times to let it sink in well

@MathsByPushkarSir 6 лет назад

Please cover transfirmation and sketching of graphs

@Radawanium 6 лет назад

Spoken clearly and explained well. Great video, thank you!

@johndadacz3500 5 лет назад

Great explanation. Not seen this before. Wish this had been shown to me when at school.

@SmokedHam444 6 лет назад

I was taught this formula with a different explanation. I don't remember what it was. Also we learned a fourth method (which can be seen in the video) called the sum and product method

@elias69420 3 года назад

So here's the algorithm: 1. Divide both sides by _a._ 2. Bring _c/a_ to the other side. 3. Add _b/2a_ to both sides. 4. Simplify the left side. 5. Take the square root on both sides. 6. Solve the linear equation.

@hsterts 5 лет назад

I always have a hard time remembering most formulas, unless I understand them intuitiely. Thanks for this ideo!

@francistan4674 5 лет назад

Having a hard time with the "v" on your keyboard?

@lorenzocortese6061 2 года назад

Finally, now i can harness the power of mathematics

@thomasklugh4345 2 года назад

Question, please... At time 9:14, you began to say, "This is the area", but then switched to, "This is the length that allows the area on the left to be equal to the area on the right." I'm not sure what you mean here by using the word "length". By "length", are you referring to the literal length of one side of each square on either side of the equals sign? Or, are you saying that this is the length we must be willing to go to, to get from the geometry on the left to the geometry on the right." Sorry if that sounds convoluted, but I'd like to know, please, what your thought process was, when you said that. Thank you ! 🙄

@realguy7808 10 месяцев назад

Like a week ago I randomly realized that the quadratuc formula was just completing the square.

@chellurivenkatasatyanaraya240 3 года назад

It is very nice video for mathematics learner's,it is very helpful and useful video because I am also till I am a learner but not a teacher or master:-CHVSN as a INDIAN

@MoyuGuy Год назад

I AM HERE PROUDLY AS A 7TH GRADER THAT DOESNT WANT TO DO THERE ENGLISH HOMEWORK READING AND DECIDED TO WATCH THIS VIDEO WHILE PLAYING GAMES TO FEEL LIKE I AM DOING SOMETHING PRODUCTIVE THANK YOU EDIT: I LOVE THIS VIDEO THANK YOU SO MUCH