Solve x2= 25/64

by inspection. There are 2 real solutions. Enter the lesser number first. Leave the answers in simplest fraction form.

(1 point)
The first solution is x=

The second solution is x =

1 answer

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 \( x = \frac{5}{8} \)