Solve x2= 25/64

Question

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 =

Answer 1

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

1. First, rewrite the equation in the form of \( x = \pm \sqrt{\frac{25}{64}} \).

2. We simplify the square root:

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

Thus, the two solutions are:

• The lesser number is \( x = -\frac{5}{8} \).
• The greater number is \( x = \frac{5}{8} \).

So, the solutions are:

The first solution is \( x = -\frac{5}{8} \).

The second solution is \( x = \frac{5}{8} \).