To solve the equation \( x^2 = \frac{25}{64} \), we can take the square root of both sides.
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Start with the equation: \[ x^2 = \frac{25}{64} \]
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Take the square root of both sides, remembering to consider both the positive and negative roots: \[ x = \pm \sqrt{\frac{25}{64}} \]
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Simplify the square root: \[ x = \pm \frac{\sqrt{25}}{\sqrt{64}} = \pm \frac{5}{8} \]
This gives us two solutions:
- \( x = \frac{5}{8} \)
- \( x = -\frac{5}{8} \)
- Finally, list the solutions in order, starting with the lesser number: \[ -\frac{5}{8}, \frac{5}{8} \]
Thus, the two real solutions are \( \boxed{-\frac{5}{8}, \frac{5}{8}} \).