To solve the quadratic equation \(x^2 + 2x - 15 = 0\), we can factor it.

1. **Factor the quadratic expression:**

   We need to find two numbers that multiply to \(-15\) (the constant term) and add to \(2\) (the coefficient of the linear term \(x\)).

   The numbers that satisfy these conditions are \(5\) and \(-3\).

2. **Rewrite the equation:**

   \[
   x^2 + 5x - 3x - 15 = 0
   \]

3. **Group the terms:**

   \[
   (x^2 + 5x) - (3x + 15) = 0
   \]

4. **Factor by grouping:**

   \[
   x(x + 5) - 3(x + 5) = 0
   \]

   Factor out the common factor \((x + 5)\):

   \[
   (x - 3)(x + 5) = 0
   \]

5. **Set each factor equal to zero:**

   \[
   x - 3 = 0 \quad \text{or} \quad x + 5 = 0
   \]

   Solving these equations gives:

   \[
   x = 3 \quad \text{or} \quad x = -5
   \]

### Final Answer:
The solutions to the equation \(x^2 + 2x - 15 = 0\) are \(x = 3\) and \(x = -5\).

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

Here are some related questions:
1. How can we solve a quadratic equation using the quadratic formula?
2. What is the method of completing the square, and how is it applied to this equation?
3. Can you explain how to determine the vertex of the quadratic function \(y = x^2 + 2x - 15\)?
4. How can we find the axis of symmetry for a quadratic equation?
5. What are the roots of a quadratic function and how are they related to the graph of the function?

**Tip:** Always check the discriminant (\(b^2 - 4ac\)) when solving quadratic equations; it tells you how many real solutions to expect.

Learn how to solve the quadratic equation x^2 + 2x - 15 with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring quadratic equations and solving equations with specific coefficients. Suitable for students in Grades 7-9.

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