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

Sep 26, 2016

$x = 12$ or $x = 6$

#### Explanation:

The difference of squares identity can be written:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

We use this later with $a = x - 9$ and $b = 3$...

First note that both sides are divisible by $4$, so let's divide both sides by $4$ to get:

$x \left(x - 18\right) = - 72$

Multiply out the left hand side and add $72$ to both sides to get:

$0 = {x}^{2} - 18 x + 72$

$\textcolor{w h i t e}{0} = {x}^{2} - 18 x + 81 - 9$

$\textcolor{w h i t e}{0} = {\left(x - 9\right)}^{2} - {3}^{2}$

$\textcolor{w h i t e}{0} = \left(\left(x - 9\right) - 3\right) \left(\left(x - 9\right) + 3\right)$

$\textcolor{w h i t e}{0} = \left(x - 12\right) \left(x - 6\right)$

Hence:

$x = 12$ or $x = 6$