# How do you solve #4 x(x - 18) = - 288#?

##### 1 Answer

Sep 26, 2016

#### Explanation:

The difference of squares identity can be written:

#a^2-b^2 = (a-b)(a+b)#

We use this later with

First note that both sides are divisible by

#x(x-18) = -72#

Multiply out the left hand side and add

#0 = x^2-18x+72#

#color(white)(0) = x^2-18x+81-9#

#color(white)(0) = (x-9)^2-3^2#

#color(white)(0) = ((x-9)-3)((x-9)+3)#

#color(white)(0) = (x-12)(x-6)#

Hence:

#x = 12# or#x = 6#