To solve the equation \( x^2 = \frac{25}{64} \), we need to take the square root of both sides.
Taking the square root, we get:
\[ x = \pm \sqrt{\frac{25}{64}} \]
We can simplify this as follows:
\[ x = \pm \frac{\sqrt{25}}{\sqrt{64}} = \pm \frac{5}{8} \]
Thus, the two solutions are:
\[ x = \frac{5}{8} \quad \text{and} \quad x = -\frac{5}{8} \]
Now, arranging the answers in order and leaving the answers in simplest fraction form, we have:
\[ -\frac{5}{8}, \frac{5}{8} \]
So the final answer is:
\[ -\frac{5}{8}, \frac{5}{8} \]
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