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Solve the equation: x2 − 5x + 6 = 0, then factor it as (x − 2) + (-3x + 6) = 0 and x(x − 2) − 3(x − 2) = 0 and x(x − 3) = 6

Mathematics

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Step-by-step solution

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Your factoring steps are correct! You've successfully factored the quadratic equation.

Here's how to complete the solution:

  1. The given equation is factored correctly.

    (x−2)(x−3)=0(x - 2)(x - 3) = 0

  2. Apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

    x−2=0orx−3=0x - 2 = 0 \quad \text{or} \quad x - 3 = 0

  3. Solve each linear equation for x.

    x−2=0  ⟹  x=2x - 2 = 0 \implies x = 2 x−3=0  ⟹  x=3x - 3 = 0 \implies x = 3

    The solutions are x=2x = 2 and x=3x = 3.

    x=2 or 3x = \boxed{2 \text{ or } 3}
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