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 $\boxed{{\displaystyle -\frac{5}{8},\frac{5}{8}}}$.