Question

What is the intermediate step in the form (x + a)2 = b as a result of completing the

square for the following equation?
x2
12x + 32 = 4

Answer 1

Given:

The equation is:

`x^2-12x+32=4`

To find:

The result of completing the square for the given equation.

Solution:

We have,

`x^2-12x+32=4`

It can be written as:

`x^2-12x=4-32`

`x^2-12x=-28`

Now, we need to add half of square of coefficient of x, to complete the square.

Adding
`((-12)/(2))^2` on both sides, we get

`x^2-12x+((-12)/(2))^2=-28+((-12)/(2))^2`

`x^2-2(x)(6)+(-6)^2=-28+(-6)^2`

`x^2-2(x)(6)+(6)^2=-28+36`
`[\because (-a)^2=(a)^2]`

Using the formula
`(a-b)^2=a^2-2ab+b^2`, we get

`(x-6)^2=8`

Therefore, the required equation after completing the square is
`(x-6)^2=8`.