Question

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

Answer 1

`x = 12` or `x = 6`

Explanation:

The difference of squares identity can be written:

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

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(x-18) = -72`

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

`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`