Question

1. $x^2 + 6 = -18$

Explanation:

Step1: Isolate the $x^2$ term

Subtract 6 from both sides.
$x^2 + 6 - 6 = -18 - 6$
$x^2 = -24$

Step2: Solve for $x$ using square roots

Take square roots of both sides, using imaginary numbers since the radicand is negative.
$x = \pm\sqrt{-24} = \pm\sqrt{4 \times 6 \times (-1)} = \pm2\sqrt{6}i$

Answer:

$x = 2\sqrt{6}i$ and $x = -2\sqrt{6}i$