# How do you solve the quadratic equation by completing the square: #5x^2 + x = −5#?

##### 1 Answer

#### Explanation:

The first thing you need to do is get the equation to the form

In your case,

In order to solve this quadratic by completing the square, you need to write the left side of the equation as the **square of a binomial** by adding a term to both sides of the equation.

This term will be determined by the *coefficient* of the **2**, then **square** the result.

In your case, you have

The quadratic can thus be written as

The left side of the equation can now be written as

This means that you have

Notice that this equation has **no real solutions**, but it does have two distinct **complex solutions**.

Take the square root of both sides to get

Use the fact that the square root of a *negative number* can be written as

In your case, the right side of the equaation is equivalent to

This means that you have

The two solutions of the quadratic will thus be