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

[@mariaplacencia1842]

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

[@ggb1377]

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

[@jamesmccamish3901]

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!

[@johnback0007]

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

[@vespa2860]

@@johnback0007 The right hand side = - 8 + 81/4 find the common denominator which leads to - 32/4 + 81/4 which gives 49/4

[@danieldennis9831]

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".

[@MsChemicalEngineer]

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.

[@marcfirst9341]

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

[@twettiet1893]

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!

[@progresskuyeri6967]

Understanding made easier ... Thank you

[@chocolateangel8743]

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.

[@TheMathManProfundities]

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.

[@Kleermaker1000]

Indeed! It is fundamentally different.

[@georgesadler7830]

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.

[@alastairgreen2077]

The square root of 4 is 2.

[@Kleermaker1000]

@@alastairgreen2077 So you must say, for example: X^2 = 16 => X = +/- squarert. 16 = +/- 4.

[@tanyatoki7967]

🌞Thank you. Great explanation.

[@israteeg752]

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.

[@jerry2357]

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

[@leetrask6042]

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

[@Kleermaker1000]

Exactly my idea. Now I need a video in which the QF is explained. It did not fall out of the blue sky, didn't it?

[@goddessqueen9626]

Thank you this is so much easy 4 me 😊

[@V1RT8]

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

[@johnback0007]

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

[@jasona716]

​@@johnback0007it's -8 + (81/4) which is the same (turning the '8' into '4ths' by multiplying it by 4) as -32/4 + 81/4 which is ( -32 + 81) / 4 which is 49 / 4

[@stainlesssteellemming3885]

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

[@theophonchana5025]

b^(2) - 4ac = 49

[@lamper2]

WHERE DID THE 49 COME FROM?

[@enriqueiii9209]

8 = 81/4 then he subtracted -8 from both sides then it was -8 + 81/4 then the denominator has to be the same 4, 4 x -8 = -32 81 -32 = 49, 49/4. hope you understand but it was confusing.

[@QueenJohniheoma-ly4bv]

Same question

[@aurorafede8682]

Could you make word math problems videos?

[@jcylasmatematicas]

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

[@kfjfkeofitorhf9520]

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

[@tonywright560]

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

[@charlesward8196]

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.

[@lakieshalewis3172]

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.

[@jeanphillippes2196]

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

[@archieosco3176]

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??

[@MrPatrick1414]

That's what I did. /2 then factored

[@CHINGGISJINNAHPHARAOH123]

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

[@harrymatabal8448]

We learnt these in high school

[@johnback0007]

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

[@gogamejoy2869]

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

[@anushkavashisth4336]

yea we all know but that is a different method and he teaching us another method.

[@VincentLauria6]

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

[@fadelali330]

X\=16--log.

[@johnbo964]

Give me a problem that can only be solved by this method.

[@lilpapi4399]

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

[@markjakeway2035]

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.

[@ramesankd1604]

Rootof2

[@tobyharnish8952]

"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.

[@MrOoofah]

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

[@lisamccray6481]

Can we laugh ALONG? In other words me too. 😂😂🤣🤣Gotta watch lots of times.

[@anushkavashisth4336]

I AM AN freshman AT Havard jst lettin you know

[@SM-ev3pv]

99% cannot do this, right?

[@theophonchana5025]

#trinomial #polynomial #QuadraticEquation

[@ruthshaw5595]

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

[@sebsnotshifty]

instructions not clear, i accidently reformed yugoslavia

[@thomassicard3733]

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

[@theophonchana5025]

a = 1 b = -9 c = 8

[@irwandasaputra9315]

x1=8 dan x2=1

[@troysmith1749]

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.

[@gtg1018]

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???

[@MosesWilfred-jw6cz]

Thanks alot you save my life 😊🥹

[@damnusename]

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. 🤷

[@Chrisp0394]

This helped me 0%, thank you so much

[@stevenscottoddballz]

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

[@MsChemicalEngineer]

It's late I know but I'd be happy to share my solution: S = -1/4, 2.