The given quadratic expression is:

\[
x^2 + 5x - 120
\]

To solve this, we need to factorize the quadratic expression.

We are looking for two numbers that multiply to give \(-120\) and add to give \(5\). After analyzing the factors of \(-120\), we find that \(15\) and \(-8\) satisfy the conditions:

\[
15 \times (-8) = -120 \quad \text{and} \quad 15 + (-8) = 5
\]

So, we can factor the expression as:

\[
x^2 + 5x - 120 = (x + 15)(x - 8)
\]

To solve for \(x\), set each factor equal to zero:

1. \(x + 15 = 0 \Rightarrow x = -15\)
2. \(x - 8 = 0 \Rightarrow x = 8\)

Thus, the solutions are:

\[
x = -15 \quad \text{or} \quad x = 8
\]

Would you like more details or have any questions about this solution?

Here are 5 related questions to expand your understanding:

1. How can you verify the solution to a quadratic equation?
2. What is the process for completing the square for a quadratic equation?
3. Can all quadratic equations be factored easily?
4. How does the quadratic formula work for solving equations that aren't factorable?
5. What is the geometric significance of the roots of a quadratic equation?

**Tip:** Always check your factored form by expanding it to ensure it matches the original equation.

Learn how to solve the quadratic equation x^2 + 5x - 120 by factoring. This step-by-step solution covers essential algebraic concepts, including factoring quadratics and identifying roots. Ideal for students in Grades 8-10.

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