Question

solve by taking square roots

1. $-3(x + 3)^2 - 10 = 20$

Explanation:

Step1: Isolate the squared term

Add 10 to both sides:
$$-3(x+3)^2 = 20 + 10$$
$$-3(x+3)^2 = 30$$

Step2: Solve for $(x+3)^2$

Divide both sides by -3:
$$(x+3)^2 = \frac{30}{-3}$$
$$(x+3)^2 = -10$$

Step3: Take square roots

Take the square root of both sides, using $i = \sqrt{-1}$:
$$x+3 = \pm\sqrt{-10}$$
$$x+3 = \pm i\sqrt{10}$$

Step4: Solve for $x$

Subtract 3 from both sides:
$$x = -3 \pm i\sqrt{10}$$

Answer:

$x = -3 + i\sqrt{10}$ and $x = -3 - i\sqrt{10}$