Question

solve the quadratic equation using the square root property.
$(x + 8)^2 = -81$
the solution set is
(simplify your answer. use a comma to separate answers as needed. type an exact answer, using radicals as needed. express complex numbers in terms of $i$)

Explanation:

Step1: Apply square root property

Take square roots of both sides:
$$\sqrt{(x+8)^2} = \pm\sqrt{-81}$$

Step2: Simplify square roots

Use $i=\sqrt{-1}$ to simplify:
$$x+8 = \pm 9i$$

Step3: Isolate x

Subtract 8 from both sides:
$$x = -8 \pm 9i$$

Answer:

$\{-8 + 9i, -8 - 9i\}$