Question

1. -8x² + 9 = 777

Explanation:

Step1: Isolate the $x^2$ term

Subtract 9 from both sides:
$$-8x^2 = 777 - 9$$
$$-8x^2 = 768$$

Step2: Solve for $x^2$

Divide both sides by -8:
$$x^2 = \frac{768}{-8}$$
$$x^2 = -96$$

Step3: Solve for $x$

Take square roots of both sides (using imaginary numbers):
$$x = \pm\sqrt{-96} = \pm\sqrt{16 \times 6 \times (-1)} = \pm4i\sqrt{6}$$

Answer:

$x = 4i\sqrt{6}$ and $x = -4i\sqrt{6}$