Question

solve by using the quadratic formula and express the solution set in exact simplified form.
$x(x + 4) = -8$
if there is more than one solution, separate the answers with commas.

the solution set is

Explanation:

Step1: Rewrite to standard quadratic form

Expand and rearrange the equation:
$x(x + 4) = -8$
$x^2 + 4x + 8 = 0$

Step2: Identify coefficients

For $ax^2+bx+c=0$, $a=1$, $b=4$, $c=8$.

Step3: Apply quadratic formula

Use $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$:
$$x=\frac{-4\pm\sqrt{4^2-4(1)(8)}}{2(1)}$$

Step4: Simplify discriminant

Calculate the radical term:
$\sqrt{16-32}=\sqrt{-16}=4i$

Step5: Simplify the expression

Substitute and reduce the fraction:
$x=\frac{-4\pm4i}{2}=-2\pm2i$

Answer:

$-2+2i, -2-2i$