# How do you solve #x^2 + 12x + 20 = 0# by completing the square?

##### 2 Answers

#### Explanation:

Our Quadratic is in the form

First, let's subtract

Half of

Simplifying, we get:

Now, we factor the left side of the equation. We think of two numbers that add up to

We can now factor this as:

Notice, what I have in blue is the same as

Taking the square root of both sides, we get:

Subtracting

#### Explanation:

By completing the square, we always half the coefficient of

Also by completing the square, we also take away the squared number of half of the previous coefficient (the number in the brackets).

Simplifying terms:

Plugging this back in, removing the

This is in the completed square form. You can always check this by expanding out:

Solving; so far we know:

So we add

As we do not want squares brackets, the opposite of squaring is square rooting, and this cancels out the squared brackets:

Always remember the

As we want

Always remember there are mostly two solutions, as there is a plus and minus on the answer.

But using our squared numbers:

These simplify to: