https://file.aiquickdraw.com/mathbot/file/17301367652122g6vwijv.jpg

To solve the equation:

\[
x^2 + 7x + 12 = 0
\]

we can use factoring.

### Step-by-Step Solution:
1. **Identify the equation**: We have a quadratic equation in the form \( ax^2 + bx + c = 0 \), where \( a = 1 \), \( b = 7 \), and \( c = 12 \).

2. **Look for factors of 12 that add up to 7**:
   - The factors of 12 are \( (3, 4) \), since \( 3 + 4 = 7 \).

3. **Rewrite the equation using these factors**:
   \[
   x^2 + 7x + 12 = (x + 3)(x + 4) = 0
   \]

4. **Set each factor equal to zero**:
   - \( x + 3 = 0 \) gives \( x = -3 \).
   - \( x + 4 = 0 \) gives \( x = -4 \).

### Solution:
The solutions to the equation are:
\[
x = -3 \quad \text{and} \quad x = -4
\]

Would you like further details or have any questions?

Here are some related questions for further exploration:
1. How do we solve quadratic equations when factoring is not possible?
2. What is the quadratic formula, and how does it work?
3. How can we verify the solutions of a quadratic equation?
4. What are real-world applications of quadratic equations?
5. How does the discriminant in the quadratic formula help in determining the nature of the roots?

**Tip:** Always double-check that the factors multiply back to the original equation to confirm accuracy.

Discover how to solve the quadratic equation x^2 + 7x + 12 = 0 using factoring. This problem involves key algebraic concepts suitable for students in Grades 7-9. Follow a detailed step-by-step solution.

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