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Hot is the opposite of

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Answer

x=2, 3x=2,\ 3

Step-by-step solution

4 steps

  1. Identify coefficients from x2−5x+6=0x^2 - 5x + 6 = 0.

    a=1a = 1, b=−5b = -5, c=6c = 6.

  2. Quadratic formula.

    x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

  3. Discriminant D=b2−4acD = b^2 - 4ac.

    D=(−5)2−4(1)(6)=25−24=1D = (-5)^2 - 4(1)(6) = 25 - 24 = 1

  4. Roots.

    x=5±12(1)=5±12x = \frac{5 \pm \sqrt{1}}{2(1)} = \frac{5 \pm 1}{2} x1=5+12=62=3x_1 = \frac{5 + 1}{2} = \frac{6}{2} = 3 x2=5−12=42=2x_2 = \frac{5 - 1}{2} = \frac{4}{2} = 2

    Final answer x=2, 3\boxed{x=2,\ 3}

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