# How do you solve using the quadratic formula x^2 - 5x - 8 = 0?

Jul 10, 2018

${x}_{1} = \frac{5}{2} \pm \frac{\sqrt{57}}{2}$

#### Explanation:

using the formula for

${x}^{2} + p x + q = 0$
${x}_{1 , 2} = - \frac{p}{2} \pm \sqrt{{p}^{2} / 4 - q}$
so we get for $p = - 5 , q = - 8$
${x}_{1 , 2} = \frac{5}{2} \pm \sqrt{\frac{25}{4} + 8}$
Note that

$\frac{25}{4} + 8 = \frac{25 + 32}{4} = \frac{57}{4}$

${x}_{1 , 2} = \frac{5}{2} \pm \frac{\sqrt{57}}{2}$