# How do you solve x^2-x-72=0?

Mar 14, 2017

$x = 9 \text{ } \mathmr{and} x = - 8$ are the two solutions.

#### Explanation:

To solve a quadratic equation (one with an ${x}^{2}$ term), there are three options:

In this case the quadratic trinomial can be factored.

${x}^{2} - x - 72 = 0 \text{ }$ find factors of 72 which differ by 1.

$\left(x - 9\right) \left(x + 8\right) = 0$

Either of the factors could be equal to $0$.

If $x - 9 = 0 \text{ "hArr" } x = 9$

If $x + 8 = 0 \text{ "hArr" } x = - 8$

$x = 9 \text{ } \mathmr{and} x = - 8$ are the two solutions.