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14x^2+19x+32=18

  • math -

    This requires some Alg II...

    Initial Problem...
    14x^2 + 19x + 32 = 18

    Move "C term" to the right.
    14x^2 + 19x = -14

    Divide both sides by 14.
    x^2 + 19x/14 = -1

    Complete the square.
    x^2 + 19x/14 + 361/784 = -1 + 361/784

    Simplify and factor...
    (x + 19/28)^2 = -423/784

    Square root both sides.
    x + 19/28 = ±i√(423/784)

    Rationalize right side.
    x + 19/28 = (±3i√47)/28

    Isolate x.
    x = -19/28 ±3i√(47)/28

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