Solve x² + 5x + 6 = 0 step by step

Mathematics

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Step-by-step solution

5 steps

To solve the quadratic equation x2+5x+6=0x^2 + 5x + 6 = 0 step by step, follow these steps:

  1. Identify the coefficients

    • a=1a = 1 (coefficient of x2x^2)
    • b=5b = 5 (coefficient of xx)
    • c=6c = 6 (constant term)

  2. Factor the quadratic

    • We need two numbers that multiply to cc (6) and add to bb (5). The numbers 2 and 3 work because 2×3=62 \times 3 = 6 and 2+3=52 + 3 = 5.
    • Thus, we can factor the equation as (x+2)(x+3)=0(x + 2)(x + 3) = 0.

  3. Set each factor to zero

    • x+2=0x + 2 = 0 or x+3=0x + 3 = 0

  4. Solve for xx

    • From x+2=0x + 2 = 0: x=−2x = -2
    • From x+3=0x + 3 = 0: x=−3x = -3

  5. Final solutions

    • The solutions to the equation x2+5x+6=0x^2 + 5x + 6 = 0 are x=−2x = -2 and x=−3x = -3.
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