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The equation to solve is:

\[
x^2 + 13x = -36
\]

First, let's move all terms to one side to set the equation equal to zero:

\[
x^2 + 13x + 36 = 0
\]

Now, we need to factor this quadratic equation. We're looking for two numbers that multiply to \(36\) (the constant term) and add up to \(13\) (the coefficient of the middle term).

The numbers are \(9\) and \(4\), since:

\[
9 \times 4 = 36 \quad \text{and} \quad 9 + 4 = 13
\]

Thus, the factored form of the equation is:

\[
(x + 9)(x + 4) = 0
\]

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

\[
x + 9 = 0 \quad \Rightarrow \quad x = -9
\]
\[
x + 4 = 0 \quad \Rightarrow \quad x = -4
\]

Thus, the solutions are:

\[
x = -9 \quad \text{and} \quad x = -4
\]

Would you like more details on factoring quadratics or have any other questions?

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Here are 5 related questions to further explore this topic:

1. How can you check if a quadratic equation is factorable?
2. What are other methods to solve quadratic equations besides factoring?
3. What is the quadratic formula, and how does it relate to factoring?
4. How can you factor trinomials with coefficients other than 1 for \(x^2\)?
5. How does completing the square help solve quadratic equations?

**Tip**: Always check your factored solution by expanding the factors to ensure they match the original quadratic equation.

Learn how to solve the quadratic equation x^2 + 13x + 36 = 0 by factoring. This step-by-step solution explores how to factor the quadratic and apply the Zero Product Property to find the solutions. Suitable for Grades 8-10 students.

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