To solve the equation \( 49x^2 - 25 = 0 \), follow these steps:

### Step 1: Move the constant term to the other side
\[
49x^2 = 25
\]

### Step 2: Divide both sides by 49
\[
x^2 = \frac{25}{49}
\]

### Step 3: Take the square root of both sides
\[
x = \pm \sqrt{\frac{25}{49}}
\]

### Step 4: Simplify the square root
\[
x = \pm \frac{5}{7}
\]

Thus, the solution is:
\[
x = \frac{5}{7} \quad \text{or} \quad x = -\frac{5}{7}
\]

Would you like more details on this solution or have any questions?

Here are 5 related questions:
1. How would you solve \( 25x^2 - 36 = 0 \)?
2. What happens if the discriminant of a quadratic equation is negative?
3. How do you solve quadratic equations using the quadratic formula?
4. How can we factor \( 49x^2 - 25 \) directly?
5. What are real-life applications of quadratic equations?

**Tip**: Always check for opportunities to factor expressions when solving quadratic equations, as it may simplify the process.

Learn how to solve the quadratic equation 49x² - 25 = 0 with a step-by-step solution. This problem demonstrates the use of the difference of squares and square root methods, covering essential algebra concepts. Suitable for students in Grades 7-9.

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