Question

9 multiple choice 10 points solve for x: $(x + 3)^2 + 5 = 1$ $x = -5$ or $-1$ $x = 13$ $x = -3 pm 2i$ $x = -3 pm 4i$

Explanation:

Step1: Isolate the squared term

Subtract 5 from both sides:
$$(x+3)^2 + 5 - 5 = 1 - 5$$
$$(x+3)^2 = -4$$

Step2: Take square root of both sides

Use the property $\sqrt{-a} = i\sqrt{a}$ for real $a>0$:
$$x+3 = \pm\sqrt{-4} = \pm 2i$$

Step3: Solve for x

Subtract 3 from both sides:
$$x = -3 \pm 2i$$

Answer:

x = -3 ± 2i