Question

solve $x^2 - 64 = 0$.

1. isolate $x^2$: $x^2 = 64$
2. apply the square root property of equality: $sqrt{x^2} = pmsqrt{64}$
3. isolate the variable:

$x = $
$x = $

Explanation:

Step1: Simplify square roots

We know that $\sqrt{x^2} = |x|$, but when we have $x^2 = 64$, taking square roots on both sides gives $\sqrt{x^2}=\pm\sqrt{64}$. Since $\sqrt{64} = 8$, we have $|x|=\pm8$, but more accurately, from $x^2 = 64$, the solutions are found by $x=\pm\sqrt{64}$.

Step2: Calculate the square root

$\sqrt{64}=8$, so the two solutions are $x = 8$ and $x=- 8$.

Answer:

$x = 8$
$x=-8$