# How do you solve 4x=x^2-45?

May 15, 2016

$\left(x - 9\right) \left(x + 4\right)$

#### Explanation:

It is a quadratic, so make it equal to 0.

${x}^{2} - 4 x - 45 = 0$

Find the factors of 45 which subtract to give 4.
The signs in the bracket are different - the greater factor will be negative.

$9 \times 5 = 45 \mathmr{and} 9 - 5 = 4$

$\left(x - 9\right) \left(x + 4\right)$