Solve the following quadratic equation by factoring -x^2+49=0

To solve the quadratic equation \(-x^2 + 49 = 0\) by factoring, follow these steps:

1. **Rewrite the equation**:  
   The equation is already in the form \(-x^2 + 49 = 0\).

2. **Move the terms**:  
   Move \(-x^2\) to the other side of the equation:
   \[
   49 = x^2
   \]
   or equivalently,
   \[
   x^2 = 49
   \]

3. **Recognize the difference of squares**:  
   Notice that \(49\) is a perfect square, so the equation can be written as:
   \[
   x^2 - 49 = 0
   \]

   This is a difference of squares, which factors as:
   \[
   (x - 7)(x + 7) = 0
   \]

4. **Set each factor to zero**:  
   Set each factor equal to zero to find the solutions:
   \[
   x - 7 = 0 \quad \text{or} \quad x + 7 = 0
   \]
   Solving these gives:
   \[
   x = 7 \quad \text{or} \quad x = -7
   \]

So, the solutions to the equation \(-x^2 + 49 = 0\) are \(x = 7\) and \(x = -7\).

Would you like more details or have any questions?

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Here are some related questions:
1. What is the difference of squares and how is it used in factoring?
2. How can you solve a quadratic equation if it's not factorable?
3. What is the significance of the signs in the quadratic equation when factoring?
4. How do you know when to use the difference of squares method?
5. How does factoring compare to using the quadratic formula?

**Tip:** When you have a quadratic equation in the form \( ax^2 - b^2 = 0 \), it can often be factored as a difference of squares, leading to \( (ax - b)(ax + b) = 0 \).

Learn how to solve the quadratic equation -x^2 + 49 = 0 by factoring. Follow a step-by-step solution method including recognizing the difference of squares. Suitable for Grades 7-9, covering key concepts in quadratic equations and factoring.

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