# How do you solve x^2 + 2x-7=0?

Apr 19, 2016

$x = - 1 \pm 2 \sqrt{2}$

#### Explanation:

Use the quadratic formula for this question where you can't find a master product that will have factors that add to the $b$ term.

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

Substitute the values into its corresponding places and evaluate.
$x = \frac{- \left(2\right) \pm \sqrt{{2}^{2} - 4 \left(1\right) \left(- 7\right)}}{2 \left(1\right)}$
$x = \frac{- 2 \pm \sqrt{4 + 28}}{2}$
$x = \frac{- 2 \pm \sqrt{32}}{2}$
$x = \frac{- 2 \pm 4 \sqrt{2}}{2}$

Simplify the terms (other than the 2 inside of the radical sign) by diving them by the common factor of 2.
$x = \frac{- 1 \pm 2 \sqrt{2}}{1}$

Answer: $x = - 1 \pm 2 \sqrt{2}$