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Solving quadratic equations by square roots | Algebra II | Khan Academy

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Solving Quadratic Equations by Square Roots
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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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Опубликовано:

21 авг 2024

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Комментарии : 301

@ashiyaprowell9563 6 лет назад

I’ve never been so confused in my life

@jaybabess_328 3 года назад

LMAOO same

@Yourfriendb3lla 3 года назад

The second he changed out the 8 for 4 and 2, I was out of the game.

@janiyiaholliday 3 года назад

I thought I was the only one

@1f2l 3 года назад

math is the most cursed subject ever

@subestacionsantamaria4794 3 года назад

@@Yourfriendb3lla Hi Isabella, but 8 is the same number 4*2, you can try to see it this way, 8 inside is made up from (2+2+2+2) or you can also see it like 2 four times....or 4 times 2, (4*2)..

@nfceastchampions2740 10 лет назад

What

@randallmokjialung3592 4 года назад

And so you've summed up my high school life

@preparator9925 3 года назад

@@randallmokjialung3592 and what will probably be my college life as well

@betheboss5972 7 лет назад

this is too confusing

@StuperStar 7 лет назад

Be The Boss True.

@iversonjoracco9266 6 лет назад

Nooo :(

@user-ic7pn9hu7y 5 месяцев назад

@@StuperStarnah i’d rather be boss baby

@ducktape4221 4 года назад

Thank you so much I was peeing during my math online class when the teacher discussed this ;-;

@ragedragon33 3 года назад

lol idk why no one except me liked this

@vivixio2737 2 года назад

@@ragedragon33 because this is the worst thing I've ever seen 💀

@woodstone7748 Год назад

Heh

@12thmanrailfans26 5 лет назад

I learn nothing from my teacher. I learn faster from an 11 minute video than a 52 minute lesson

@cameronaustin527 5 лет назад

12thman Railfans same

@divinesison6154 4 года назад

trueee

@zaniyahlovely 4 года назад

preach.

@Ravi-pr6fj 3 года назад

SAME

@phatyoshi9867 Год назад

same bro

@-smp-scientificmethodpersp838 5 лет назад

@5:13 for those of you who got lost, because he didn't explain what he was doing. He substituted one of his solutions for the x in the original solution, because he had solved for x. Since he solved for x, he can substitute what he solved for instead of using x. X=solution to be replaced with in substitution. The answer to the solution is to find what = 0. Well, 0=0 , so you have to prove that. In order to prove it, you need to get get rid of that unknown variable that needs to be solved for. In this case, it's x that is the unknown. So what do we do in algebra? Find X! After we know what x is, we can solve the original problem by replacing that x (unknown) with what we solved x to be (now known). Now we can solve the original problem. The original problem is 0=0 and you have to solve for that. The square root part in this video isn't to solve the problem (0=0). The whole square rooting part is to solve for x (X=?). Then use the answer for what x is to solve the original problem. If you still don't understand.... Yikes! Go watch some pre-algebra videos.

@alexswinton4978 2 года назад

My brain doesn’t like big paragraphs

@hannahahaha575 2 года назад

@@alexswinton4978 BAHAHA SAME

@Nataliah12 11 месяцев назад

Thank you so much for your amazing effort of explaining ❤

@Chaosflyex98 12 лет назад

Hi Mr. Khan, thank you very much for doing this for the millions of people out there watching your videos. I'm taking Algebra I and this is helping a ton! I always move towards your videos when I am about to learn something or don't understand a new concept. God bless you, again I truly thank you very much. Keep up the amazing videos! ^_^

@Bladesrcool 7 лет назад

Who needs a high school diploma?

@Alexis-kd9tm 7 лет назад

people that want a job

@mattf.868 7 лет назад

Alexis Puente Well if algebra 1 or the regents in this case is holding you back for like 2 years I suppose you can go to trade school which I think doesn't need a high school diploma ( I dunno if that's true)

@neoz.9886 6 лет назад

You need to pass the ALG EOC to get a high school diploma if I'm correct...

@gusskipner9809 5 лет назад

This is algebra 2

@xianflora8411 4 года назад

Highschoolers

@cyodissnips8086 4 года назад

Me at the end of the video not understanding any of it: wut Him: Well, that was a good warm up

@i6zl135 4 года назад

it be like that

@ducktape4221 4 года назад

Ikr

@OffTheBeatenPath_ 9 лет назад

Really poor example to use the square root method.

@stevenf5902 6 лет назад

OffTheBeatenPath Why?

@Roblafo 5 лет назад

@@stevenf5902 because 8 doesn't square root into just a number so he had to write it weird which is confusing for most people trying to learn this.

@Reagandover1 5 лет назад

Yeah I’m trying to learn the actual method but he’s doing a bunch of different ones he does factoring aaaa

@PsychoEye 5 лет назад

@@Roblafo that was right since it wasnt a perfect square

@jewellpetalcorin3093 4 года назад

2x²=7 is much better example

@heyitsjaee222 6 лет назад

my brain has so much smoke coming out of it 😐

@VanNintendo 8 лет назад

You are awsome! You have helped me so much whenever I have a test!

@sarahskup 12 лет назад

THIS HELPED SOOOO MUCH!!!!!! IM IN 7TH GRADE AND AM TAKING ALGEBRA 1, BUT I PROBABLY WOULD NOT HAVE PASSED PRE- ALGEBRA WITHOUT THIS GUY!!!!!!!! YOU RULE MR. KHAN

@ethanellis7864 2 года назад

your doing solving quadratic equations by taking roots in seventh grade? I'm genuinely curious because I'm in 10th lol

@ethanellis7864 2 года назад

wait a sec. i didnt even realize this was from nine years ago. holy cow

@sarahskup 2 года назад

@@ethanellis7864 haha seeing your reply was funny I’m 22 now and don’t even remember making this comment

@sarahskup 2 года назад

@@ethanellis7864 but yeah I was in an advanced math program so I was a few years ahead back then

@sarahskup 2 года назад

@@ethanellis7864 these videos really got me though honestly

5 лет назад

over doing it can be confusing ...

@teachmechannel6828 6 лет назад

Thank you so much for this great lesson. I was searching so hard for this kind of extracting square root, then I found this video. THANK YOU SO MUCH😇

@debo3822 4 года назад

Imagine this, but explained MORE complicated than it should be. Thats my teacher y'all

@vchivaaree 8 лет назад

waaaaa. I don't understand anything

@user-kq4np7se2h 8 лет назад

Just use the x2 for square root and divide 8 into 4x2

@rochellezhaynesabac5243 7 лет назад

i didnt understand a single thing

@kaygee8260 6 лет назад

Rochelle Zhayne Sabac You need to know some other concepts about quadratics to fully understand this

@kevinalex-pq2sh 3 года назад

me neither lol

@anshugupta000 6 лет назад

Sir please make a video how to factroise. √3x² + 10x - 8√3 = 0

@nightowl538 2 года назад

It's been 11 yrs but generations still use it till now

@memuggleman 9 лет назад

What do you do with a problem like: 2x^2-12x+18=32? I don't know how to do the 2x^2 part

@hairlessopossum4042 6 лет назад

memuggleman lmao sorry a little late bate take the squre root of it making it have not exponent. If negative use the original answer if it were positive and add i

@justintimeboi31 6 лет назад

Y'all are answering his question 3 years late.

@shaz85vw 12 лет назад

Mr. Khan Your an absolute god send! Thanks so much Its been 10 yrs since i finished yr 12 and ive decided to go to university and do an associate degree of engineering and the text book we have to use is sooo mumbo jumbo and pretty relentless, but your explainations are brilliant. Thank you ever so much. Shannon

@wowo6460 4 года назад

shaz85vw did you graduate bro?

@i6zl135 4 года назад

its been almost 10 years, are you good bro?

@NathanRio79 2 года назад

I think "shaz85vw"is still an active (or at least rarely active) RU-vid Account. This account has a "Favorites" Created Playlist and the latest video in the playlist is from October 2020.

@dollyspine 2 года назад

helping me pass my final exam tomorrow, THANK YOU

@yuinurahilyon5711 5 лет назад

Bizarre equation. Me: glad you know.

@airasagmon262 Год назад

im from philippines Thank u sm I might Ace the math exam tommorow thanks to u😂

@jlklai98 12 лет назад

If only my teacher could be as good and clear in Algebra as Mr. Kahn. Thanks for the little clarification!!!

@janiyabeene6200 2 года назад

Thank you so much. I have a quiz tmr and I was bound to fail. Now I feel much more confident!

@shimonmaneshwar1218 Год назад

How did it go?

@tanjirokamado892 Год назад

howd it go

@woodstone7748 Год назад

HOW DID IT GO

@eeeeeehrg Год назад

HOW DID IT GO???!?

@tigrrlily2569 4 года назад

I have a test tmr and am trying to drill this information into my head but I'm honestly so confused help...

@hudsongoff8922 4 года назад

Tigrrlily25 how’d it go?

@tigrrlily2569 4 года назад

@@hudsongoff8922 Oh I actually got 100%! It wasn't as hard as I'd expected it was going to be.

@repentnowjesusiscomingsoon7356 Год назад

Romans 1:16 For I am not ashamed of the Gospel for it is the power of God unto salvation to every one that believes.

@blessings1063 2 года назад

10 minutes of nothing overcomplicating simple things and not explaining the confusing stuff

@madmaxout0 8 лет назад

i was taught differently

@Mark-jh4mt 7 лет назад

Thanks! Helped me alot, the last two equations are not taught to my class yet so i might get a head start from this! Thanks again!

@diegocordero676 5 лет назад

You're doing all the easy ones

@saxofan9972 6 лет назад

Thank you. This really help me a lot

@tanyanathani 9 месяцев назад

I have a quiz tomorrow this really helped me, I wish my teacher thought like this otherwise I wouldn’t have to self learn every time I go home

@user-no8cu3jh6o 3 месяца назад

This was so easy and clear to understand idk why people seem confused

@despiadado3447 3 года назад

thank you so much i have a algebra 2 mid test due in 2 hours

@MelissaMachine5000 11 лет назад

Who else is here for Algebra HW

@user-kq4np7se2h 8 лет назад

FINALLY I GOT IT!

@ItsHayden 7 лет назад

idk why but to me this guy sorta sounds like Yandere Dev

@ashtonhartis7480 Год назад

thank you this didn't help as much as I wanted it to. but it did help a lil bit thank you

@bananiaman3162 9 лет назад

Thanks a lot! This really saved my a$$ :)

@Tenshar1 13 лет назад

Thank you so much, because it was just not clicking with me at all....God bless you!!!!

@pmpdaddy Год назад

off the addy rn feeling good preciate it khan

@YasiaAliyah 8 лет назад

Im confused on the last equation. Why would we subtract 1? Is it because of x squared?

@aarnavslesh7890 4 года назад

I think so

@Kelvinnyakundib 3 года назад

Good

@cadepriola5075 2 года назад

Sounds like Andre from The League✊

@1f2l 3 года назад

what app do you use to write?

@cherryson4625 3 года назад

Tmro is my maths test thanks soo much

@timbarrett8803 11 лет назад

I just bombed a test on this, and now it makes so much sense! Thanks!

@adijoshi4751 Год назад

it's wild to think this videos 11 years old

@johnpuri4317 7 лет назад

How to solve with 1/3 power? e.g (1+x)^(1/3) + (1-x)^(1/3) = 2^(2/3)

@tobisteindl951 7 лет назад

1/3 power is like the third root of something. So you have to find 3 equal parts that multiply up to that number. For example 8^1/3 is 2 because 2^3 is 8

@brooklynnmetz8767 8 лет назад

I really must figure out what program he runs for the "chalk board". It would come very handy at one point or another

@aarnavslesh7890 4 года назад

It would

@14hazel 6 лет назад

Why do they even teach this in school. We arent even gonna be using these formulas in our everyday life -_-

@heyyitsvero1775 5 лет назад

Ikr

@12thmanrailfans26 5 лет назад

that's what im sayin

@subhashpoonia8193 2 года назад

I am from INDIA🇮🇳. And watching for 10th class exam📄. But shocked to see the time of uploading the video. 11 years ago 👇. 👇🏼

@patrciaclemons8183 Год назад

I learn this in 1 week at college, get tested, and never look at it again. What is education

@keilynrobison8002 6 лет назад

thanks your really helpful

@lilivrse5794 5 лет назад

This is exactly how our teacher discussed it

@anydragon4811 4 года назад

i had one question and you answered it in the first 2 minutes

@purr2564 3 года назад

TY OMGG

@cheery_cherry6756 3 года назад

9:00 can you use the quadratic formula to solve these still?

@scorpionkiller8408 Год назад

thank you so much i just got my test result in math my score is 39/50 yay

@kadapi1972 11 лет назад

as x-8 = 0 or x-2=0, in solving, the answers turn out to be positive 8 and 2

@MexicanCat999 11 лет назад

why can't you replace my Algebra 2 teacher?!

@anasaleem1 5 лет назад

Khan acadmy always blown up my mind give a like if u agree

@munchlady1670 8 лет назад

what if you have two different letters all together like r^2-8t+24=0

@facebookteam7494 8 лет назад

it's the same

@SG-ho7xb 5 лет назад

It would not be a quadratic equation

@celiodochka8027 Год назад

my test is in 20 minutes and i’m confused, hope this helps

@OMGitsANJA 12 лет назад

my thoughts exactly

@maxferia2714 10 лет назад

Woot I finally get this

@TheJunkieBox 14 лет назад

Haha, I did all this Algebra I stuff about a month ago. This would have been really nice then. >xP

@TheKarakRecords 7 лет назад

good meme

@gamechip06 3 года назад

This dude is 11 years older than when he made this comment

@gavinbriggs2020 5 лет назад

Thank you! Wish my teacher could teach like you...

@krishis2286 4 года назад

I lost it at 4:53 but whatever

@16letter68 4 года назад

they subtituted the value of x i think

@maximocaceres4685 2 года назад

Love your videos

@realyours643 4 года назад

thankyou so much

@jyugonanbaka4344 4 года назад

So what will you do if you have the ax2 + bx + c=0 form rather than ax2 + c form?

@lorcanzo2498 Год назад

Did you find out?

@erikawhite5582 8 лет назад

what if the equation is -3(x^2-1)=121

@kylamartinez4100 7 лет назад

can someone teach me how to solve 3x^2+1=28

@SG-ho7xb 5 лет назад

@mouthfulasouth Год назад

I need the last step!!! Solving the square root part because that's not explained in any other video 😫

@bulletprooff1k 11 лет назад

At 8:52 how did the negative 8 and 2 turn positive?

@jennifercano1541 11 лет назад

Awesome

@black3ru 2 года назад

math kills my braincells haha

@ashitbhagat2510 7 лет назад

great

@shrushtivipinmota.1977 6 лет назад

finally I got it

@LexiiCharms 11 лет назад

I want you to know that you are saving my life. Thank you so much.

@RemotHuman 10 дней назад

why isn't sqrt[(4x+1)^2] absolute value |4x+1|

@ustinzafranski6634 4 года назад

oh yeah yeah

@AKJaglan 4 года назад

how can we find root of a^2=110+√a

@users4007 2 года назад

1 hour class is a waste of time when i could simply watch a 10 minute video and understand subject better

@marshalltoby6994 3 года назад

i have a test in less than thirty minutes and im extremely sure i wont pass the test nor this school year

@Vi.0.9 3 года назад

so did you pass it or not

@marshalltoby6994 3 года назад

@@Vi.0.9 i did but i cheated so HAHA-

@jonasward5977 3 года назад

@@marshalltoby6994 Congratulations, on passing, while some may say cheating is wrong, I would argue forcing kids to learn this crap is even more wrong. I hate math so much.

@marshalltoby6994 3 года назад

@@jonasward5977 thank you! i hope math this year and in the future is treating you well. im currently procrastinating on math by checking all my notifs 😔

@woodstone7748 Год назад

HAHAHA

@valerialopez6725 2 года назад

Not me deciding to study 30 minutes before my test ☠️

@FunWithAaron 12 лет назад

Crystal clear now! I feel like watching all of your videos. It's like you go from being dumb, to being a genius after watching just one! Lol

@stiarait 8 лет назад

what?

@bigbruno822 8 лет назад

Ikr

@sandervanvelzen3333 9 месяцев назад

I tried to solve (x+5)^2=(2x-3)^2 by taking the square root. However it doesn't seem to work, as i don't know how to get the two solutions. I only get 1 solution which is 8. Does anyone know why this doesn't work?