https://file.aiquickdraw.com/mathbot/file/17250413179354b0urstx.jpg

Let's solve the given equation from the image:

### Equation

The equation provided is:

\[
16x^2 - 49 = 0
\]

### Solution Steps

1. **Rewrite the equation to identify a pattern:**

   Notice that this equation is a difference of squares. The difference of squares formula is:

   \[
   a^2 - b^2 = (a - b)(a + b)
   \]

   We can rewrite the equation \(16x^2 - 49 = 0\) in the form of a difference of squares:

   \[
   (4x)^2 - 7^2 = 0
   \]

2. **Apply the difference of squares formula:**

   \[
   (4x - 7)(4x + 7) = 0
   \]

3. **Set each factor equal to zero and solve for \(x\):**

   - For the first factor \(4x - 7 = 0\):

     \[
     4x = 7 \implies x = \frac{7}{4}
     \]

   - For the second factor \(4x + 7 = 0\):

     \[
     4x = -7 \implies x = -\frac{7}{4}
     \]

4. **List the solutions:**

   The solutions to the equation are:

   \[
   x = \frac{7}{4} \quad \text{or} \quad x = -\frac{7}{4}
   \]

### Conclusion

The correct answer is **D) \( x = \frac{7}{4} \) or \( x = -\frac{7}{4} \)**.

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

Here are 5 related questions that might interest you:

1. How do you solve quadratic equations using the quadratic formula?
2. What are the properties of a difference of squares?
3. How can you solve equations that are not factorable by simple methods?
4. What are the steps to graph a quadratic equation?
5. How do you find the vertex of a parabola from a quadratic equation?

**Tip:** Recognizing patterns like the difference of squares can simplify solving quadratic equations significantly.

Learn how to solve the quadratic equation 16x^2 - 49 = 0 with a detailed step-by-step solution. This problem involves using the difference of squares formula and covers key algebraic concepts. Suitable for students in Grades 7-9.

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