To solve the equation \( x^2 = \frac{25}{64} \) by inspection, we can take the square root of both sides.
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First, rewrite the equation in the form of \( x = \pm \sqrt{\frac{25}{64}} \).
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We simplify the square root:
\[ x = \pm \frac{\sqrt{25}}{\sqrt{64}} = \pm \frac{5}{8} \]
Thus, the two solutions are:
- The lesser number is \( x = -\frac{5}{8} \).
- The greater number is \( x = \frac{5}{8} \).
So, the solutions are:
The first solution is \( x = -\frac{5}{8} \).
The second solution is \( x = \frac{5}{8} \).