# How do you solve x^2-7x-6=0 using the quadratic formula?

Aug 10, 2015

$x = \frac{7 + \sqrt{73}}{2}$ or $x = \frac{7 - \sqrt{73}}{2}$

#### Explanation:

The quadratic formula states that for a quadratic equation $a {x}^{2} + b x + c$, its roots, $x$ can be computed as $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Consider the quadratic equation ${x}^{2} - 7 x - 6 = 0$. It has coefficients $a = 1$, $b = - 7$ and $c = - 6$. To solve for $x$, we plug these numbers into the quadratic formula.

$x = \frac{- \left(- 7\right) \pm \sqrt{{\left(- 7\right)}^{2} - 4 \left(1\right) \left(- 6\right)}}{2 \left(1\right)}$
$x = \frac{7 \pm \sqrt{73}}{2}$

Hence, $x = \frac{7 + \sqrt{73}}{2}$ or $x = \frac{7 - \sqrt{73}}{2}$