Extracting the Square Root 1. 9x ^ 2 - 25 = 0

The equation is:

\[
9x^2 - 25 = 0
\]

Let's solve it step by step:

### Step 1: Move the constant to the other side
\[
9x^2 = 25
\]

### Step 2: Divide both sides by 9 to isolate \(x^2\)
\[
x^2 = \frac{25}{9}
\]

### Step 3: Take the square root of both sides
\[
x = \pm \sqrt{\frac{25}{9}} = \pm \frac{5}{3}
\]

### Final Solution:
\[
x = \frac{5}{3} \quad \text{or} \quad x = -\frac{5}{3}
\]

Would you like more details on any step or have questions?

Here are 5 related questions:
1. How do you solve similar quadratic equations with different coefficients?
2. Can you solve \(4x^2 - 16 = 0\)?
3. What happens if you cannot take the square root of a negative number?
4. How can you complete the square to solve quadratic equations?
5. What are the real and complex solutions of \(x^2 + 1 = 0\)?

**Tip:** When solving equations, always isolate the variable before applying operations like square roots or division!

Learn how to solve the quadratic equation 9x^2 - 25 = 0 by isolating the variable and applying square roots. This problem involves algebraic concepts like quadratic equations and square roots. Suitable for students in Grades 8-10.

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