Question

After inspection, what are the two real solutions to x^2 = 25/64. Enter the lesser number first, and leave the answer in simplest fraction form

Answer 1

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

The solutions will be:

\[
x = \pm \sqrt{\frac{25}{64}}
\]

Calculating the square root, we have:

\[
\sqrt{\frac{25}{64}} = \frac{\sqrt{25}}{\sqrt{64}} = \frac{5}{8}
\]

Thus, the two solutions are:

\[
x = \frac{5}{8} \quad \text{and} \quad x = -\frac{5}{8}
\]

To list the solutions in order with the lesser number first, we write:

\[
-\frac{5}{8}, \frac{5}{8}
\]

Therefore, the final answer in simplest fraction form is:

\[
-\frac{5}{8}, \frac{5}{8}
\]