# How do you solve m^2+ 2m - 24 = 0?

Apr 17, 2016

The solutions are:

$m = 4$
$m = - 6$

#### Explanation:

${m}^{2} + 2 m - 24 = 0$

The equation is of the form color(blue)(am^2+bm+c=0 where:

$a = 1 , b = 2 , c = - 24$

The Discriminant is given by:

$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(2\right)}^{2} - \left(4 \cdot 1 \cdot \left(- 24\right)\right)$

$= 4 + 96 = 100$

The solutions are found using the formula:

$m = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$m = \frac{\left(- 2\right) \pm \sqrt{100}}{2 \cdot 1} = \frac{\left(- 2 \pm 10\right)}{2}$

$m = \frac{- 2 + 10}{2} = \frac{8}{2} = 4$

$m = \frac{- 2 - 10}{2} = - \frac{12}{2} = - 6$