Question

Solve for x. Select all solutions.
x^2 - 64 = 0
A) -8
B) 0
C) 8
D) 64

Answer 1

To solve the equation \( x^2 - 64 = 0 \), we can start by adding 64 to both sides:

\[
x^2 = 64
\]

Next, we take the square root of both sides. Remember that taking the square root gives us both the positive and negative roots:

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

Since \(\sqrt{64} = 8\), we have:

\[
x = 8 \quad \text{or} \quad x = -8
\]

Thus, the solutions to the equation \( x^2 - 64 = 0 \) are \( x = 8 \) and \( x = -8 \).

Now, let's look at the answer choices:
- A) -8 (this is a solution)
- B) 0 (not a solution)
- C) 8 (this is a solution)
- D) 64 (not a solution)

Therefore, the correct solutions are:
**A) -8 and C) 8.**