Question

Complete the square to transform the quadratic equation into the form (x – p)2 = q. x2 - 12x - 5 = 7

Answer 1

x^2 - 12x - 5 = 7
x^2 - 12x = 7 + 5
x^2 - 12x = 12
x^2 - 12x + 36 = 12 + 36
(x - 6)^2 = 48 <====

Answer 2

The completing square form of given equation is
`(x-6)^2=48`

Explanation:

Given:
`x^2-12x-5=7`

We need to change given quadratic equation in completing square form.

`(x-p)^2=q`

`x^2-12x-5=7`

First we add 5 both sides

`x^2-12x-5+5=7+5`

Add both sides square of half of coefficient of x

`x^2-12x+36=36+12`

`(x-6)^2=48`

Now we compare the equation to completing square

`(x-p)^2=q\rightarrow (x-6)^2=48`

`p\rightarrow 6`

`q\rightarrow 48`

Hence, The completing square form of given equation is
`(x-6)^2=48`