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Quadratic Solver

Solve ax² + bx + c = 0 with the quadratic formula — every step shown and explained, including the discriminant and simplified radicals.

x² − 5x + 6 = 0
  1. 1

    Identify a, b, and c.

    a = 1, b = -5, c = 6

  2. 2

    Compute the discriminant, b² − 4ac.

    D = (-5)² − 4(1)(6)

    D = 25 − 24 = 1

  3. 3

    Write the quadratic formula and substitute.

    x = ( −b ± √D ) / 2a

    x = ( 5 ± √1 ) / 2

  4. 4

    √D is a whole number, so simplify each root.

    √1 = 1

    x = ( 5 + 1 ) / 2 = 3

    x = ( 5 − 1 ) / 2 = 2

Solution

x = 3 or x = 2