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Math Help - a^2+ab+c=0

  1. #1
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    wolfv
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    Question a^2+ab+c=0

    I think this is solvable, but I am stuck.

    Given a^2+ab+c=0
    solve for a.

    Thanks for your help.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: a^2+ab+c=0

    Hint: Use the quadratic formula.
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  3. #3
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    Re: a^2+ab+c=0

    hint:

    a^2 + ab + c = a^2 + ab + \frac{b^2}{4} + c - \frac{b^2}{4} = \left(a + \frac{b}{2}\right)^2 + c - \frac{b^2}{4}
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: a^2+ab+c=0

    a^2+ab=-c

    4a^2+4ab=-4c

    4a^2+4ab+b^2=b^2-4c

    (2a+b)^2=b^2-4c

    2a+b=\pm\sqrt{b^2-4c}

    2a=-b\pm\sqrt{b^2-4c}

    a=\frac{-b\pm\sqrt{b^2-4c}}{2}
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  5. #5
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    Re: a^2+ab+c=0

    Thanks MarkFL2 and Deveno. The Quadratic equation is quite useful and has a whole page on wikipedia.
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