# How do you solve the inequality |x^2+6x+16|<8?

Dec 12, 2015

$x \in \left(- 4 , - 2\right) \subset \mathbb{R}$

#### Explanation:

$- 8 < {x}^{2} + 6 x + 16 < 8$

${x}^{2} + 6 x + 24 > 0 \mathmr{and} {x}^{2} + 6 x + 8 < 0$

${\Delta}_{1} = 36 - 4 \cdot 24 < 0$, so the parabola doesn't cross x-axis.

Delta_2 = 36 - 4 * 8 = 4 Rightarrow x_0 = (-6 ± 2)/2

$x \in \mathbb{R} \mathmr{and} - 4 < x < - 2$