# How do you solve x^2 - x - 30 = 0 using the quadratic formula?

Feb 24, 2016

#### Answer:

See below for use of quadratic formula to obtain
$x = - 5 \mathmr{and} x = 6$

#### Explanation:

For the general quadratic equation $a {x}^{2} + b x + c = 0$
the quadratic formula:
$\textcolor{w h i t e}{\text{XXX}} x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
gives the solutions.

For the example: ${x}^{2} - x - 30 = 0$
$\textcolor{w h i t e}{\text{XXX}} a = 1$
$\textcolor{w h i t e}{\text{XXX}} b = - 1$
$\textcolor{w h i t e}{\text{XXX}} c = - 30$

Replacing the variables $a , b , c$ in the general solution formula gives:
$\textcolor{w h i t e}{\text{XXXX}} x = \frac{- \left(- 1\right) \pm \sqrt{{\left(- 1\right)}^{2} - 4 \left(1\right) \left(- 30\right)}}{2 \left(1\right)}$

$\textcolor{w h i t e}{\text{XXXX}} = \frac{1 \pm \sqrt{121}}{2}$

$\textcolor{w h i t e}{\text{XXXX}} = \frac{1 \pm 11}{2}$

$\Rightarrow x = - 5 \mathmr{and} + 6$