Question

solve the quadratic equation using the square root property.
$(x + 9)^2 = -16$
the solution set is {}.
(simplify your answer. use a comma to separate answers as needed. type an exact answer, using radicals as needed. exp

Explanation:

Step1: Apply square root property

Take square roots of both sides:
$$\sqrt{(x+9)^2} = \sqrt{-16}$$
$$x+9 = \pm\sqrt{-16}$$

Step2: Simplify imaginary root

Rewrite $\sqrt{-16}$ as $4i$ (since $\sqrt{-1}=i$):
$$x+9 = \pm4i$$

Step3: Solve for x

Subtract 9 from both sides:
$$x = -9 \pm4i$$

Answer:

$\{-9+4i, -9-4i\}$