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How do I solve the quadratic equation x² + 5x + 6 = 0?
To solve x² + 5x + 6 = 0, I'll use factoring:
Step 1: Find two numbers that multiply to give 6 and add up to 5.
These numbers are 2 and 3 (2×3=6 and 2+3=5)
Step 2: Rewrite the equation as factored expression.
x² + 5x + 6 = 0
x² + 2x + 3x + 6 = 0
x(x + 2) + 3(x + 2) = 0
(x + 3)(x + 2) = 0
Step 3: Set each factor equal to zero and solve.
x + 3 = 0 → x = -3
x + 2 = 0 → x = -2
The solutions are x = -3 and x = -2
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