# How do you solve #x^2=12x-45# by completing the square?

##### 1 Answer

#### Explanation:

Start by getting the

Now you need to focus on writing the left side of the equation as a **square of a binomial** by adding a term to both sides of the equation.

The *coefficient* of the **2**, then **square** the result to get

This means that you must add

The left side of the equation can now be written as

The equation becomes

You can tell right away that this equation has **no real solutions**, so you're going to have to use *complex numbers* to get the solutions you want.

Take the square root of both sides to get

Now, the square root of a negative number can be written, using the fact that

In your case, you have

Therefore,

The two solutions to your quadratic will thus be