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The given equation is:

\[
x^2 - 64 = 0
\]

We can solve this by first adding 64 to both sides:

\[
x^2 = 64
\]

Now, take the square root of both sides:

\[
x = \pm \sqrt{64}
\]

\[
x = \pm 8
\]

So, the solutions for \( x \) are \( x = 8 \) and \( x = -8 \).

From the provided options, the correct answers are:

- \( 8 \)
- \( -8 \)

Would you like any further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the general method for solving a quadratic equation like \( x^2 - c = 0 \)?
2. How does the process change when solving equations like \( x^2 + c = 0 \)?
3. Why do we take both the positive and negative roots when solving \( x^2 = c \)?
4. Can this method be used for solving any quadratic equation? Why or why not?
5. How does factoring compare to using the square root method for solving quadratics?

**Tip:** Always check for multiple solutions when solving equations involving squares, as both positive and negative roots may exist!

Solve for x. Select all solutions: x^2 - 64 = 0.

Learn how to solve the quadratic equation x^2 - 64 = 0 by applying the square root property. This problem demonstrates key algebraic techniques for finding the solutions to x^2 = c, resulting in x = ±8.

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