To solve the equation \( x^2 - 64 = 0 \), we can start by isolating \( x^2 \):
\[ x^2 = 64 \]
Next, we take the square root of both sides. Remember that taking the square root can yield both a positive and a negative solution:
\[ x = \pm \sqrt{64} \]
Calculating the square root gives us:
\[ x = \pm 8 \]
Thus, the solutions for \( x \) are:
\[ x = 8 \quad \text{and} \quad x = -8 \]
So, the final answer is \( x = 8 \) or \( x = -8 \).