# How do you solve #x^2 + 6x + 10 = 0# by completing the square?

##### 2 Answers

#### Explanation:

Completing the square is a method of getting as close as you can with one set of brackets and adding or subtracting the rest.

It ends up in a form like

As you can see this is pretty close to the original quadratic. All you need to do is add

To then solve, rearrange like so

There is no solution for the given equation for any

#### Explanation:

Consider the standard form of

The by completing the square we have:

In your case

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The coefficient of

Thus the vertex is a minimum and above the x-axis

Thus there is no solution for

However their will be a solution for

Given that

Updated: The

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This becomes:

Multiply by (-1)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This becomes:

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Solution for