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Math Help - Completing the square.

  1. #1
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    Completing the square.

    I need to solve this equation by completing the square:

    2x^2 + x - 8 = 0

    In my textbook the answer is x = 1.77 or x = -2.27

    I've tried to do it but can't get the right answer...
    2x^2 + x - 8 = 0
    x^2 + 0.5x - 4 = 0
    x^2 + 0.5x = 4
    x^2 + 0.5x + 0.0625 = 4.0625
    (x + 0.0625)^2 = 4.0625
    x + 0.0625 = (+/-)sqrt4.0625
    x = - 0.0625 + sqrt4.0625 or x = - 00625 - sqrt4.0625
    x = 1.95... or x = -2.07...

    Thanks.
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  2. #2
    Super Member Aryth's Avatar
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    Ok, so we have the equation:

    2x^2 + x - 8 = 0

    Step 1: Move the term without an x to the other side of the equation:

    2x^2 + x = 8

    Step 2: get the x^2 term by itself by dividing by its coefficient:

    x^2 + \frac{1}{2}x = 4

    Step 3: Set aside the coefficient of the x-term and divide it in half:

    \frac{\frac{1}{2}}{2} = \frac{1}{4}

    Step 4: Square the answer:

    \left(\frac{1}{4}\right)^2 = \frac{1}{16}

    Step 5: Add the square to both sides:

    x^2 + \frac{1}{2} + \frac{1}{16} = \frac{65}{16}

    Step 6: Set up the factored form:

    \left(x + \frac{1}{4}\right)^2 = \frac{65}{16}

    Step 7: Take the square root of both sides:

    x + \frac{1}{4} = \pm \frac{\sqrt{65}}{4}

    Step 8: Separate the plus and minus:

    x + \frac{1}{4} = \frac{\sqrt{65}}{4}

    x + \frac{1}{4} = -\frac{\sqrt{65}}{4}

    Step 9: Solve each equation:

    x = \frac{\sqrt{65}-1}{4}

    x = -\frac{\sqrt{65}+1}{4}

    Put the fractions in the calculator and you get:

    x \approx 1.7655 \approx 1.77

    x \approx 2.2655 \approx 2.27

    And there you go.
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  3. #3
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    Thankyou very much.

    I think I went wrong when I should have had (x + 1/4)^2 but I had (x + 1/16)^2.
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