Let's solve the quadratic equation \(x^2 + 2x - 15 = 0\).

### Factoring Method

We'll first check if the quadratic can be factored.

We're looking for two numbers that multiply to \(-15\) (the constant term) and add up to \(2\) (the coefficient of the middle term).

The numbers \(5\) and \(-3\) fit this requirement because:
- \(5 \times -3 = -15\)
- \(5 + (-3) = 2\)

So, we can factor the quadratic equation as:

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

### Solving for \(x\)

Now, set each factor equal to zero:

1. \(x + 5 = 0 \Rightarrow x = -5\)
2. \(x - 3 = 0 \Rightarrow x = 3\)

### Solutions

The solutions are \(x = -5\) and \(x = 3\).

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

Here are 5 related questions you might find useful:
1. What is the quadratic formula, and how do you use it to solve \(x^2 + 2x - 15\)?
2. How do you verify the solutions of a quadratic equation?
3. What are the roots of a quadratic equation, and how are they related to its graph?
4. How do you complete the square for the quadratic equation \(x^2 + 2x - 15\)?
5. How can you determine the vertex of the parabola \(y = x^2 + 2x - 15\)?

**Tip:** When factoring a quadratic equation, always double-check the product and sum of the factors to ensure they match the original equation.

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 using the quadratic formula. Suitable for students in Grades 7-9.

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