To solve the equation \( x^2 = \frac{25}{64} \) by inspection, we can take the square root of both sides.
The equation can be rewritten as:
\[ x = \pm \sqrt{\frac{25}{64}} \]
Calculating the square root:
\[ \sqrt{\frac{25}{64}} = \frac{\sqrt{25}}{\sqrt{64}} = \frac{5}{8} \]
Thus, the solutions are:
\[ x = \frac{5}{8} \quad \text{and} \quad x = -\frac{5}{8} \]
Now, listing the solutions in order from lesser to greater:
The first solution is:
\[ x = -\frac{5}{8} \]
The second solution is:
\[ x = \frac{5}{8} \]
So the final answers are:
The first solution is \( x = -\frac{5}{8} \)
The second solution is \( x = \frac{5}{8} \)