solve x^2 = 25/64• there are two real solutions. enter the lesser number first. leave the answers in simplest fraction form.

{__,__}

1 answer

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

  1. Taking the square root: \[ x = \pm \sqrt{\frac{25}{64}} \]

  2. Simplifying the square root: \[ x = \pm \frac{\sqrt{25}}{\sqrt{64}} = \pm \frac{5}{8} \]

Thus, the two real solutions are:

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

Listing the lesser solution first, we have:

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