To solve the equation \( x^2 = \frac{25}{64} \), we can take the square root of both sides.
Remember that taking the square root will give us both the positive and negative solutions:
\[ x = \pm \sqrt{\frac{25}{64}} \]
Now, we simplify the right side:
\[ \sqrt{\frac{25}{64}} = \frac{\sqrt{25}}{\sqrt{64}} = \frac{5}{8} \]
Thus, the solutions for \( x \) are:
\[ x = \frac{5}{8} \quad \text{and} \quad x = -\frac{5}{8} \]
Since we need to list the lesser solution first, the two real solutions are:
\[ -\frac{5}{8}, \frac{5}{8} \]
Therefore, the final answer is:
\[ -\frac{5}{8}, \frac{5}{8} \]