Question

Find all solutions first 25x^2 - 16 = 0

Answer 1

To solve the equation \( 25x^2 - 16 = 0 \), we can start by isolating the term with \( x^2 \).

1. **Add 16 to both sides**:
\[
25x^2 = 16
\]

2. **Divide both sides by 25**:
\[
x^2 = \frac{16}{25}
\]

3. **Take the square root of both sides**:
\[
x = \pm \sqrt{\frac{16}{25}}
\]

4. **Simplify the square root**:
\[
x = \pm \frac{\sqrt{16}}{\sqrt{25}} = \pm \frac{4}{5}
\]

Thus, the solutions to the equation \( 25x^2 - 16 = 0 \) are:
\[
x = \frac{4}{5} \quad \text{and} \quad x = -\frac{4}{5}
\]

These are all the solutions.