# How do you factor #x^ { 2} + 6 x - 27= 0#?

##### 2 Answers

#### Explanation:

To factor

Find to numbers whose product is -27 and whose sum is 6. For this it is -3 and 9.

Rewrite the equation as:

Factor the first 2 terms:

Factor the last 2 terms:

So now we have:

Notice we can bracket off this and factor out the expressions in parenthesis:

These are our required factors:

#### Explanation:

Given:

#x^2+6x-27#

Here are a couple of methods:

**Method 1 - Fishing for factors**

Find a pair of factors of

The pair

So we find:

#x^2+6x-27 = (x+9)(x-3)#

**Method 2 - Completing the square**

#x^2+6x-27 = x^2+6x+9-36#

#color(white)(x^2+6x-27) = (x+3)^2-6^2#

#color(white)(x^2+6x-27) = ((x+3)-6)((x+3)+6)#

#color(white)(x^2+6x-27) = (x-3)(x+9)#