Question

1. what is the solution set of the equation $x^2 - 64 = 0$?

a) {8, -8}
b) {8}
c) {4, -4}
d) {4}

Explanation:

Step1: Rewrite the equation

We start with the equation \(x^{2}-64 = 0\). We can rewrite this equation as \(x^{2}=64\) by adding 64 to both sides of the equation.

Step2: Solve for x

To solve for \(x\), we take the square root of both sides. Remember that if \(x^{2}=a\) (where \(a\geq0\)), then \(x=\pm\sqrt{a}\). So for \(x^{2} = 64\), we have \(x=\pm\sqrt{64}\). Since \(\sqrt{64}=8\), then \(x = 8\) or \(x=- 8\). So the solution set is \(\{8,-8\}\).

Answer:

a) {8, -8}