How to Complete The Square….Step-by-Step…. 

I never felt so confused the way that you explained this quadratic situation.

I think this explanation confused me more than helped! Solved it easily and was very confused by the solution modeled!

Excellent, best CTS video I've seen. Really appreciated the overview and contrasting of different approaches to solving a QE. You get a smiley face and four stars to make you feel extra special!

You're a very good teacher. I was never much for arithmetic, but I love mathematics. I think you do a great job of explaining how to do the problems.

I remember this from school over 40 yrs ago. Remembering (a-b)^2=a^b-2ab+b^2 means forming a a^2-2ab+b^2 on one side. Funnily enough, my first instinct was to multiply by 2 to make 4x^2 etc. But factoring out 2 is easier lol. Thanks for reminding me of this technique. Isolating a^2-2ab to one side and adding +b^2 to both sides "completes the square".

I tried your MENU, bacon and egg, and it killed my logarithmic nemesis. What a teacher you are. Thanks for creating this platform where we could come and have a refreshing drink. Bravo!

You know, this would make more sense if you taught it using an area model. This allows you to see why you divide the "b term" in half and square it. You should also consider doing a video on the Po-Shen Loh method for solving equations, making sure to use a graph when explaining it. You could also use an area model to introduce students to the P-Q Formula. I recently learned about it from people outside the U.S. It's like a condensed version of the Quadratic Formula. I prefer it.

Understanding made easier ... Thank you

🌞Thank you. Great explanation.

Do you have notes for a college class MAC1105 it’s focused on algebra graphing. I seen the algebra notes just didn’t know if it would cover quadratic equations etc.

Thank you this is so much easy 4 me 😊

I just wrote -9x as -8x-x and did some algebra, but i understand your goal with this equation...good job!!

Que manera de complicarse para resolver una ecuación cuadrática sencilla...Cuál era el objetivo: resolver la ecuación o demostrar como se el completamiento cuadrático??

I don't remember using the CTS method while taking Algebra way back when, so I guess it's a new technique placed thereafter. Be that as it may, I don't see the purpose for it over factoring or the QF , since CTS is very sloppy and prone to mistakes.

Could you make word math problems videos?

Thank you for another powerful video on Completing the Square, however, the square of four is 2. Since x is square, we have two solutions for these type of problems.

I find it easier with the quadratic formula. However I wish to thank you for the video, outstanding as always. 👍😊

I'm just wondering why you would complete the square for this example, when it factorises very simply to (x-1)(x-8)=0?

I need to look at this again, at least twice. Black magic.

Bit like that Paddington Bear story where he was trying to make a 4-legged table level.

Granted, I’ve been out of college for about 35 years now, but I have to say that when I was taught algebra in high school, I was taught factoring and the quadratic formula, but, until today, I have never heard of completing the square. I don’t see how it adds anything to what I was taught.

Why would you CTS this? It's an "in your head" factoring to (x-8)(x-1)=0

I need help please. How do I do this one? [S² + 7/4S - 1/2]

WHERE DID THE 49 COME FROM?

Couldn't you just factor x^2 - 9x+8=0 into (X-1)(x-8)=0 ? That being the case (X-1)= 0 therefore X=1 or (X-8) = 0; therefore X = 8. Same answer, a lot easier; in the case where poly = 0??

#trinomial #polynomial #QuadraticEquation

b^(2) - 4ac = 49

Completing the square in the general case is how the quadratic formula is derived.

There is a technical issue with the way you handle square roots. The root sign refers only to the principal square root. For roots of positive real numbers this is of course the positive root. So √4=2 not ±2. The correct approach would be to say things such as x²=4⇒x=±√4=±2. To say √(x²)=√4 is true but eliminates one of the solutions and √(x²)=±√4 adds nothing to this as one principal root cannot be the negative of another.

Anyone, how did he gets 49/4 from 81/4, i can figure it ou, please explain.

Instructor: milking it for 18min Me: x=1 in less than a second

So, I solved the original equation by factoring, and quickly arrived at values of X as X = (1,8) HOWEVER, as convoluted as C.T.S. Is, I can see where it would allow the solution of equations that did not factor to whole numbers. Another tool for the box, that I will need to learn how to use and keep sharp.

We learnt these in high school

You should have selected and equation that could not be easily factored. I solved it in my head by factoring in about 2 femtoseconds

Hello sir, just one question what if the coefficient or any number in the quadratic equation is NOT divisible by 2 (unless you want a decimal) eg.3,9,21,7, etc. really want to know Thank you, sir

instructions not clear, i accidently reformed yugoslavia

Watching these videos makes me sleepy quicker than Ambien!!!

You have completed the square to solve an equation, but what you have not covered is just completing the square of a quadratic expression. In fact this video may have students dividing through by the coefficient in x squared when it is not an equation leading to errors.

X\=16--log.

2/2=1 18/9 16/2=8 1-9+8= -8+8=0 X=1

"quadratic always have two solutions" -- Incorrect. Consider this one: x^2+4x+4 = 0 (x+2)(x+2) = 0 x = -2 There is my proof.

I AM AN freshman AT Havard jst lettin you know

Actually there is easy solution for this equation. where x=1 or x=8 : (x-1)(x-8)=0

The way you illustrated and explained this left me completely confused.

99% cannot do this, right?

Good lord! I solved the equation in my head in about 10 seconds. NO FRACTIONS NECESSARY!!! and basically 3 steps to the solution. CTS is NOT the way to solve this one. Simple factoring for this one: FACTOR 2x^2 - 18x + 16 into 2(x^2 - 9x + 8) = 0 Divide each side by 2 FACTOR x^2 - 9x + 8 and you get (x - 1)(x - 8) = 0 Divide each side of that (above) by one of the binomial terms, then divide that (above) by the other binomial to get each term isolated, thus: x - 1 = 0 x - 8 = 0 SIMPLE x = 1 or x = 8

Once you mention the quadratic formula, why don't you just describe and explain that and you keep on explaining factoring? What if the solutions are imaginary numbers???

What did I just watch? Is this deliberately the most complicated way to solve a quadratic equation? You'd run out of time in an exam if you had to do them all that way. 🤷

a = 1 b = -9 c = 8

This helped me 0%, thank you so much

Thanks alot you save my life 😊🥹