CTS and general solution

Question 1

whats the CTS method to find the THIRD term (in the below case y)
x^2 + 2xy +y^2 = (x+y)^2

Answer 1

1)look for the coeffiecient of x
2)divide coefficient by 2
3)square the number

Question 2

x^2 + 8x + ___

Answer 2

x^2 + 8x + 4^2 = (x+4)^2

coefficieny of x is 8
divide it by 2 –> 4
square it –> 4^2

Question 3

how to solve quadratic equations by CTS

Answer 3

1) reduce the coefficient of x^2 to one. Also known as the monic form (basically some equations will have like 3x^2 then u need change to 3(x^2)

2) divide the 2nd term by 2 and get a + and a - of it squared (eg. +(5/2)^2 - (5/2)^2

3)the first one with the + become the identity then the one with the - js add at the back