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Solve x^2 - 5x + 6 = 0

Worked through step by step. More quadratics.

Answer
x=2,x=3\boxed{x = 2, x = 3}

Substituting x=2x = 2 and x=3x = 3 back into the original equation both yield 0=00 = 0, confirming the solutions are correct.

Problem: Solve the quadratic equation x2−5x+6=0x^2 - 5x + 6 = 0.

Steps

  1. Factor the quadratic expression
    (x−2)(x−3)=0(x - 2)(x - 3) = 0
  2. Apply the zero product property
    x−2=0orx−3=0x - 2 = 0 \quad \text{or} \quad x - 3 = 0
  3. Solve for x
    x=2orx=3x = 2 \quad \text{or} \quad x = 3

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