Question

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

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 $(\dfrac{-12}{2})^2$ on both sides, we get

$x^2-12x+(\dfrac{-12}{2})^2=-28+(\dfrac{-12}{2})^2$

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

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

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 $(x-6)^2=8$.