Question

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

Answer 1

To solve the quadratic equation \( x^2 + 5x + 6 = 0 \), we can use various methods such as factoring, using the quadratic formula, or completing the square. Here, I'll demonstrate the factoring method since this equation factors easily.

1. **Factor the quadratic**: We need to find two numbers that multiply to the constant term (6) and add up to the coefficient of the \( x \) term (5). The numbers that satisfy these conditions are 2 and 3.

Thus, we can factor the equation as:
\[
(x + 2)(x + 3) = 0
\]

2. **Set each factor to zero**: Now, we can set each factor equal to zero to find the solutions for \( x \):
\[
x + 2 = 0 \quad \text{or} \quad x + 3 = 0
\]

Solving these equations gives:
\[
x = -2 \quad \text{and} \quad x = -3
\]

3. **Write the solutions**: The solutions to the equation \( x^2 + 5x + 6 = 0 \) are:
\[
x = -2 \quad \text{and} \quad x = -3
\]

Therefore, the final answer is \( x = -2 \) and \( x = -3 \).