Question

X^2 -6x - 15 = 0
complete the square

Answer 1

Recalling that

`(x-a)^2=x^2-2ax+a^2`

Let's compare the middle term:

`-6x = -2ax \iff a=3`

So, we want to complete

`(x-3)^2 = x^2-6x+9`

Which differs from
`x^2-6x-15` by 24. So, if we add 24 to both sides, we have

`x^2-6x-15=0 \iff x^2-6x+9=24 \iff (x-3)^2=24`

Answer 2

(x - 3)^2 = 24.

Explanation:

x^2 -6x - 15 = 0

(x - 3)^2 - 9 - 15 = 0

(x - 3^2 -24 = 0

(x - 3)^2 = 24.