The given quadratic equation is:

\[
x^2 + 2x - 63 = 0
\]

### To solve this, we can use factoring:

We are looking for two numbers that multiply to give \(-63\) and add up to \(2\).

Factors of \(-63\) that add up to \(2\) are \(9\) and \(-7\), since:

\[
9 \times (-7) = -63 \quad \text{and} \quad 9 + (-7) = 2
\]

So, the equation factors as:

\[
(x + 9)(x - 7) = 0
\]

### Solving for \(x\):

\[
x + 9 = 0 \quad \text{or} \quad x - 7 = 0
\]

This gives:

\[
x = -9 \quad \text{or} \quad x = 7
\]

### Final solutions:
\[
x = -9 \quad \text{or} \quad x = 7
\]

Do you want more details on any part of this solution? 

Here are 5 related questions you might explore:
1. How do you verify the solutions of a quadratic equation?
2. What if a quadratic equation cannot be factored easily?
3. How can you solve quadratic equations using the quadratic formula?
4. What is the relationship between the discriminant and the nature of the roots?
5. How do you complete the square to solve a quadratic equation?

**Tip:** Always check your factored equation by expanding it to ensure you didn't miss any terms!

Learn how to solve the quadratic equation x² + 2x - 63 by factoring. This step-by-step solution demonstrates how to factor and apply the zero product property. Ideal for students in Grades 8-10, covering important algebraic concepts.

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