Question

solve x^2 = 25/64. there are two real solutions. enter the lesser number first. leave the answers in simplest fraction form

Answer 1

To solve the equation \( x^2 = \frac{25}{64} \), we can take the square root of both sides.

1. Start with the equation:
\[
x^2 = \frac{25}{64}
\]

2. Take the square root of both sides, remembering to consider both the positive and negative roots:
\[
x = \pm \sqrt{\frac{25}{64}}
\]

3. Simplify the square root:
\[
x = \pm \frac{\sqrt{25}}{\sqrt{64}} = \pm \frac{5}{8}
\]

This gives us two solutions:
- \( x = \frac{5}{8} \)
- \( x = -\frac{5}{8} \)

4. Finally, list the solutions in order, starting with the lesser number:
\[
-\frac{5}{8}, \frac{5}{8}
\]

Thus, the two real solutions are \( \boxed{-\frac{5}{8}, \frac{5}{8}} \).