To solve the equation \( x^2 = \frac{25}{64} \) by inspection, we can take the square root of both sides.
Taking the square root gives:
\[ x = \pm \sqrt{\frac{25}{64}} \]
This can be simplified:
\[ \sqrt{\frac{25}{64}} = \frac{\sqrt{25}}{\sqrt{64}} = \frac{5}{8} \]
Thus, we have two solutions:
\[ x = \frac{5}{8} \quad \text{and} \quad x = -\frac{5}{8} \]
When listing the solutions with the lesser number first, we get:
\[ -\frac{5}{8}, \frac{5}{8} \]
Therefore, the two real solutions are:
\[ -\frac{5}{8}, \frac{5}{8} \]
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