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Math Help - more quadratics.

  1. #1
    Newbie
    Joined
    Apr 2007
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    Melbourne, Australia. Love it.
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    more quadratics.

    yeah, i know, im stuck again.
    please help me, i was never good at quadratics! and i hate completing the square.

    thankyou!!



    Factorise using the method of completing the square:

    x^2 + 5x - 11
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  2. #2
    Junior Member
    Joined
    Mar 2007
    Posts
    56
    I can help you with this.

    You can solve this problem by using the quadratic formula, but since you need to do it by completing the square I'll show you how to do it that way.

    x^2 + 5x -11 = 0

    a = x^2, b = 5x, and c = -11

    1) add c to the other side

    x^2 + 5x = 11

    2) multiply b by 1/2 and then take the square root

    [5(1/2)] = (5/2)^2 = 25/4 = b

    3) add b to both sides

    x^2 + 5x + 25/4 = 11 + 25/4

    4) factor the left side and add the right side

    (x + 5/2)^2 = 69/4

    5) take the square root of both sides and simplify

    x + 5/2 = +/-sqrt(69/4)

    x + 5/2 = +/- sqrt(69)/2

    6) subtract 5/2 on both sides

    x = -5/2 +/- sqrt(69)/2

    x = (-5 +/- sqrt(69))/2
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