Question

How do I solve the quadratic equation x^2 + 5x + 6 = 0?

Answer 1

To solve the quadratic equation \( x^2 + 5x + 6 = 0 \), you can use factoring, completing the square, or the quadratic formula. In this case, we will use factoring since it appears to be factorable.

1. **Factor the quadratic**:
We want to express \( x^2 + 5x + 6 \) as the product of two binomials. We look for two numbers that multiply to 6 (the constant term) and add up to 5 (the coefficient of \( x \)). The numbers 2 and 3 work:

\( (x + 2)(x + 3) = 0 \)

2. **Set each factor to zero**:
Now we can set each factor equal to zero:

\[
x + 2 = 0 \quad \text{or} \quad x + 3 = 0
\]

Solving these gives:

\[
x = -2 \quad \text{or} \quad x = -3
\]

3. **Conclusion**:
The solutions to the quadratic equation \( x^2 + 5x + 6 = 0 \) are:

\[
x = -2 \quad \text{and} \quad x = -3
\]