Solve x^2=25/64.

There are two real solutions. Enter the lesser number first.
Leave the answers in simplest fraction form.

3 answers

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

Remember that taking the square root will give us both the positive and negative solutions:

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

Now, we simplify the right side:

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

Thus, the solutions for \( x \) are:

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

Since we need to list the lesser solution first, the two real solutions are:

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

Therefore, the final answer is:

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

simplify the fraction form

The solutions we found, \(-\frac{5}{8}\) and \(\frac{5}{8}\), are already in their simplest fraction form, as 5 and 8 have no common factors other than 1.

Thus, the final simplified solutions remain:

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

If you have any further questions or need additional assistance, feel free to ask!