# How do you solve x² = 5x + 10 using the quadratic formula?

Mar 16, 2018

#### Explanation:

Let's put the variables and the numbers on one side.

We have:

${x}^{2} - 5 x - 10 = 0$ Since this quadratic equation is in the form $a {x}^{2} + b x + c = 0$, $a = 1$, $b = - 5$ , and $c = - 10$

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 \left(a\right) \left(c\right)}}{2 a}$ Plug in the values.

$\implies x = \frac{- \left(- 5\right) \pm \sqrt{{\left(- 5\right)}^{2} - 4 \left(1\right) \left(- 10\right)}}{2 \cdot 1}$

$\implies x = \frac{5 \pm \sqrt{25 + 40}}{2}$

$\implies x = \frac{5 \pm \sqrt{65}}{2}$

$\implies x = \frac{5 \pm \sqrt{65}}{2}$

Your two answers would be $\frac{5 - \sqrt{65}}{2}$ and $\frac{5 + \sqrt{65}}{2}$