To solve the equation \( x^2 = \frac{25}{64} \) by inspection, we want to find values of \( x \) such that when squared, they equal \( \frac{25}{64} \).
We can observe that:
\[ x = \pm \frac{5}{8} \]
This is because:
\[ \left(\frac{5}{8}\right)^2 = \frac{25}{64} \quad \text{and} \quad \left(-\frac{5}{8}\right)^2 = \frac{25}{64} \]
Therefore, the two real solutions are:
\[ -\frac{5}{8} \quad \text{and} \quad \frac{5}{8} \]
The lesser number first gives us the final answer:
\[ -\frac{5}{8}, \frac{5}{8} \]