To solve the quadratic equation \(x^2 + 3x = -2\), we first rewrite it in standard form by moving all terms to one side:

\[
x^2 + 3x + 2 = 0
\]

Now we solve it using factoring.

We need two numbers that multiply to give 2 (the constant term) and add to give 3 (the coefficient of \(x\)):

- The numbers 1 and 2 work because \(1 \times 2 = 2\) and \(1 + 2 = 3\).

Thus, we can factor the equation as:

\[
(x + 1)(x + 2) = 0
\]

Now, apply the zero-product property by setting each factor equal to zero:

\[
x + 1 = 0 \quad \text{or} \quad x + 2 = 0
\]

Solving these:

\[
x = -1 \quad \text{or} \quad x = -2
\]

Therefore, the solutions are:

\[
x = -1 \quad \text{and} \quad x = -2
\]

Let me know if you would like more details or explanations!

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Here are 5 related questions to explore further:

1. How would you solve a quadratic equation using the quadratic formula?
2. What is the discriminant of a quadratic equation and how is it used?
3. Can all quadratic equations be factored like this?
4. How would the solutions change if the equation were \(x^2 + 3x = 2\)?
5. What happens when the discriminant is negative?

**Tip:** When factoring, always check for common factors before attempting more complex methods.

Learn how to solve the quadratic equation x^2 + 3x = -2 using factoring. This step-by-step solution covers key concepts like rewriting the equation, factoring, and applying the zero-product property. Ideal for students in Grades 7-9.

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