Impress your Math Teacher! Solve by Completing The Square 

Thank you for your in depth analysis of how to solve quadratic equation using completing the square methods.

THANK YOU in all languages of the world greetings from Yemen

If I were to have to solve this equation I probably use the formula, but this is a good exercise in completing the square hand and understanding algebraic operations

Thank you!❤😂

My answer I got from completing the square was ⇒x=(-5±√33)/4 I admit that completing the square is my weakest skill in dealing with quadratic equation solving. My first step was dividing the equation by 2 to make the A coefficient 1 (ax²+bx+c=0). Then move the constant to the other side. x²+5/2x=1/2 Let's make it 10/4 as the B coefficient and make it 16ths on the other side and then add 25/16 to both sides (perfect square). x²+10/4x+25/16=8/16+25/16 factor the left and simplify the right (x+5/4)²=33/16 find square root of each side (remembering it is ± on the right) x+5/4=±√33/4. move the 5/4 to the other side and simplify x=(-5±√33)/4 Let's try the quadratic formula to check this. x=(-b±√b²-4ac)/2 x=-5±√(25-4(2)(-1)/2(2) x=(-5±√33)/4 This checks. So that is the answer. But this took me forever -- I would have preferred the quadratic formula as this would have been much faster.

When you remove the square root of 33 over 4 why does the 4 not also become + and - too.

ever since learning the quadratic equation I forgot other methods! so I searched internet and relearned completing the square. 2X^2 + 5X - 1 = 0 2X^2 + 5X = 1 X^2 + (5/2)X = 1/2 X^2 + (5/2)X + (25/16) = (1/2) + (25/16) (X + (5/4))^2 = ((8/16) + (25/16)) (X + (5/4)) = sqrt(33/16) (X + 5/4) = +/- (1/4)(sqrt(33)) X = -(5/4) +/-(1/4)(sqrt(33)) = (1/4)(-5 +/-(sqrt(33)) = -(5/4) +/- sqrt (33/16) VERIFY I'll use the quadratic equation... i.e. ( -b +/- sqrt (b^2 -4ac))/2a a = 2 b = 5 c = -1 so.... (-5 +/- sqrt (5^2 -(4)(2)(-1))/ (2)(2) (-5 +/- sqrt (25 + 8))/4 (-5 +/- sqrt (33))/4 (-5/4 +/- sqrt (33/16) ✔️✔️✔️ or -5/4 = -1.25 sqrt(33/16) = sqrt(2.062) = 1.436 -1.25 +/- 1.436 -1.25 + 1.436 = 0.186 root1 -1.25 - 1.436 = -2.686 root2 VERIFY 2X^2 + 5X - 1 = 0 root.1 X = 0.186 (2)(0.186)^2 + (5)(0.186) - 1 =? 0 0.069 + 0.93 - 1 ?= 0 0.999 - 1 ?= 0 ✔️✔️✔️ root.2 X = -2.686 2X^2 + 5X - 1 = 0 (2)(-2.686)^2 + (5)(-2.686) - 1 ?= 0 14.429 - 13.43 - 1 ?= 0 0.999 - 1 ?= 0 ✔️✔️✔️

Really helpful video! But the long intro was dragging on and on unnecesarily ;P

The perfect √square root is 4

What an incredibly good teacher!! Thank you so much John.

I enjoyed this 1:43

You turned the left side of the equation into a perfect trinomial square. That's how it's done.👍

What you did here, is it actually to create the proof of the quadratic formula??

Density

This is the first time that the answer makes no sense regarding how it was arrived at by the teacher. The rule is that whatever you do to one side of the equation, you must do to the other. I have know idea how the 5/2X is converted to 5/4 by in essence,3 removing the X and multiplying by 2? That is a violation of basic math, the variable must be accounted for, yet in his explanation it is nonexistent. I got the first part easily: X squared + 5/2X = 1/2, but it goes into nonsense for me. I might need to "brush" up on basic algebra, but I'm a College graduate with a Degree in Biochemistry and Biology w/ emphasis on Integral Calculus. Please help, where have I gone wrong? Granted, I'm 67 and graduated in 1980. but still, this hurts!!

Technically the x² part doesn't need to be 1, any square number will do. I found the numbers much easier to deal with by doubling the original equation (2x² + 5x - 1 = 0) to get (4x² + 10x - 2 = 0) and proceeding the rest the same way. Meant I was dealing with numbers over 4 instead of numbers over 16.

Insoluble.

Logical

Lost me when he divided by 2!

When its has lot of ,exponents ,roots in denominator,power : people has to know the properties 😅.

I am going to go and drink some wobbly pops catch you tomorrow

How9/4?

The quadratic formula would have been faster but the CT was required

I've been watching all the videos I can on quadratic equations and I can't understand it. Everyone who teaches this teaches it like you already know how to do it. No one really takes the time to explain it step for step and when they do they never explain why it is done that way. Why you do this step in this exact order. Why do we divide by two, why do we have to divide everything by 2 separately, things like that. Sadly after weeks of trying i don't think I'm ever going to figure this stuff out. Do you have any videos where you explain this stuff in greater detail?

☝🏻I would have enjoyed math more had the question AND answer then breakdown how you came to the conclusion...my brain seems to work backwards much like dyslexia but in its own recognition 🤷🏻‍♀️ 💁🏻‍♀️My "struggle" would be (did i forget to mention my brain works in its own way and inaccurately🙄) : 2X × 1 = 2 2X × 2 = 4 2 + 4 = 6 6 - 5 = 1

Thanks for this. But, No explanation as to why you half the x coefficient. And square. Just like many demonstrations it glosses over the fundamentals of maths. Better to show this graphically and then show that the quadratic equation is derived from completing the square. Also no mention of the fact that you can use completing the square to find the turning point of the quadratic.

WTF!!

Too much ineffective talk.

Too long and complicated. Better to skip this and focus on other math tools.

Waste of time. Use quadratic formula. Easy