Answer
$x=\frac{−3±\sqrt{17}}{2}$
$x=-1$
$x=-2$
Work Step by Step
If $|x| = c$, then $x = c$ or $x = -c. (c>0)$
$x^2+3x=2$ (equation 1) or $x^2+3x=-2$ (equation 2)
Solve using the quadratic formula
$x=\frac{−b±\sqrt{b^2−4ac}}{2a}$
Equation 1:$x^2+3x=2$
Subtract $2$ to both sides:
$x^2+3x-2=2-2$
$x^2+3x-2=0$
$a=1$, $b=3$, $c=-2$
$x=\frac{−3±\sqrt{3^2−(4⋅1⋅-2)}}{2⋅1}$
$x=\frac{−3±\sqrt{9−(-8)}}{2}$
$x=\frac{−3±\sqrt{17}}{2}$
Equation 2:
$x^2+3x=-2$
Add $2$ to both sides:
$x^2+3x+2=-2+2$
$x^2+3x+2=0$
$a=1$, $b=3$, $c=2$
$x=\frac{−3±\sqrt{3^2−(4⋅1⋅2)}}{2⋅1}$
$x=\frac{−3±\sqrt{9−(8)}}{2}$
$x=\frac{−3±\sqrt{1}}{2}$
$x=\frac{−3+1}{2}$ or $x=\frac{−3-1}{2}$
$x=-1$ or $x=-2$
