How do you solve x^2 + 2x + 13 = -8?

Jul 11, 2017

See below.

Explanation:

Adding $8$ to both sides,

${x}^{2} + 2 x + 21 = 0$

Let's use the quadratic formula, as factoring will not work in this case.

$x = \setminus \frac{- 2 \setminus \pm \setminus \sqrt{{2}^{2} - 4 \left(1\right) \left(21\right)}}{2} = \setminus \frac{- 2 \setminus \pm \setminus \sqrt{- 80}}{2} = \setminus \frac{- 2 \setminus \pm 4 \setminus \sqrt{- 5}}{2} = \setminus \frac{- 2 \setminus \pm 4 i \setminus \sqrt{5}}{2} = - 1 \setminus \pm 2 i \setminus \sqrt{5}$