Question

solve by using the quadratic formula.
$x^2 = -8x - 18$
separate your answers with commas, if necessary.
express the solution set in exact simplest form.
the solution set is { }.

Explanation:

Step1: Rewrite to standard quadratic form

$x^2 + 8x + 18 = 0$

Step2: Identify a, b, c values

$a=1,\ b=8,\ c=18$

Step3: Substitute into quadratic formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
$x = \frac{-8 \pm \sqrt{8^2 - 4(1)(18)}}{2(1)}$

Step4: Calculate discriminant

$\sqrt{64 - 72} = \sqrt{-8} = 2i\sqrt{2}$

Step5: Simplify the expression

$x = \frac{-8 \pm 2i\sqrt{2}}{2} = -4 \pm i\sqrt{2}$

Answer:

$-4 + i\sqrt{2},\ -4 - i\sqrt{2}$