Question

solve by taking square roots

1. $-3x^2 = 75$

Explanation:

Step1: Isolate $x^2$ term

Divide both sides by $-3$:
$$\frac{-3x^2}{-3} = \frac{75}{-3}$$
$$x^2 = -25$$

Step2: Take square roots of both sides

Use square root property $\sqrt{x^2} = \pm x$:
$$x = \pm\sqrt{-25}$$
Rewrite using imaginary unit $i = \sqrt{-1}$:
$$x = \pm 5i$$

Answer:

$x = 5i$ and $x = -5i$