What is the solution set for 9x^2 - 25 = 0?

Answer 1

To solve for the variable \( x \) in the equation \( 9x^2 - 25 = 0 \), we can follow these steps:

1. Add 25 to both sides of the equation to get the quadratic on one side:

\( 9x^2 = 25 \)

2. Divide both sides by 9 to isolate \( x^2 \):

\( x^2 = \frac{25}{9} \)

3. Take the square root of both sides to solve for \( x \). Don't forget that we need to consider both the positive and negative square roots:

\( x = \pm \sqrt{\frac{25}{9}} \)

4. Simplify the square root:

\( x = \pm \frac{\sqrt{25}}{\sqrt{9}} \)

\( x = \pm \frac{5}{3} \)

So the solution set for the equation \( 9x^2 - 25 = 0 \) is \( x = \frac{5}{3} \) and \( x = -\frac{5}{3} \).