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Solve Quadratic Equation: x² + 5x + 6 = 0
Published on October 7, 2024
Algebra
Solve the quadratic equation x² + 5x + 6 = 0. Factoring the equation, we find the solutions are x = -2 and x = -3.
Question
Solve the quadratic equation: x² + 5x + 6 = 0
Answer
Here’s how to solve the quadratic equation x² + 5x + 6 = 0 step-by-step:
1. Factor the quadratic expression.
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Find two numbers that add up to 5 (the coefficient of the x term) and multiply to 6 (the constant term).
- The numbers 2 and 3 satisfy these conditions: 2 + 3 = 5 and 2 * 3 = 6.
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Rewrite the equation using these numbers:
(x + 2)(x + 3) = 0
2. Set each factor equal to zero.
- x + 2 = 0
- x + 3 = 0
3. Solve for x in each equation.
- x + 2 = 0 --> x = -2
- x + 3 = 0 --> x = -3
Therefore, the solutions to the quadratic equation x² + 5x + 6 = 0 are x = -2 and x = -3.