Question

Complete the square to transform the quadratic equation into the form

(x – p)^2 = q. x^2 - 8x - 10 = 18
A) (x - 8)^2 = 14
B) (x - 4)^2 = 44
C) (x - 8)^2 = -14
D) (x - 4)2 = -44

Answer 1

The square of a binomial is written like

`(x\pm a)^2 = x^2\pm 2ax + a^2`

In your case, you have
`2ax=-8x`, which implies
`a=-4`

So, we want to write

`(x-4)^2 = x^2-8x+16`

But our left hand side is

`x^2-8x-10`

If we add 26 to both sides, we have

`x^2 - 8x - 10 +26 = 18+26 \iff x^2-8x+16=44 \iff (x-4)^2=44`