Question

what are the solutions to $2(x + 1)^2 = -36$? options: $-1 pm 2isqrt{3}$, $1 pm 3isqrt{2}$, $-1 pm 3isqrt{2}$, $1 pm 2isqrt{3}$

Explanation:

Step1: Isolate the squared term

Divide both sides by 2:
$$(x+1)^2 = \frac{-36}{2} = -18$$

Step2: Take square root of both sides

Use $\sqrt{-1}=i$ to simplify:
$$x+1 = \pm\sqrt{-18} = \pm\sqrt{9\times2\times(-1)} = \pm3i\sqrt{2}$$

Step3: Solve for x

Subtract 1 from both sides:
$$x = -1 \pm 3i\sqrt{2}$$

Answer:

-1 ± 3i√2 (matches the orange option: $\boldsymbol{-1\pm 3i\sqrt{2}}$)