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Math Help - Rearranging the GEH Statistical Equation

  1. #1
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    Rearranging the GEH Statistical Equation

    Hi,

    I use the GEH statistical equation in my line of work - traffic engineering.

    The equation is as follows:

    Rearranging the GEH Statistical Equation-capture.jpg

    I would like to rearrange the equation such that "M"is on one side of the equation and GEH and "C" are on the other side of the equation. I am finding it very difficult to do.

    Could anyone assist me with this please?

    Thanks,

    Toby
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  2. #2
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    Re: Rearranging the GEH Statistical Equation

    Hey tobyshadow.

    We get:

    GEH^2 = 2(M-C)^2/[M+C]
    GEH^2*[M+C} = 2(M-C)^2
    GEH^2*M + GEH^2*C = 2[M^2 - 2MC + C^2]
    M[GEH^2 + 4C] = 2M^2 + 2C^2

    M = [2M^2 + 2C^2]/[GEH^2 + 4C]
    = 2M^2/[GEH^2 + 4C] + 2C^2/[GEH^2 + 4C]

    Let a = 2/[GEH^2 + 4C] and c = 2C^2/[GEH^2 + 4C]

    then we have the quadratic equation:

    aM^2 - M + c = 0 which will have either no real solutions, one real solution, or two real solutions.

    Depending on the context of the situation and on the C and GEH values, if you get two solutions you will probably eliminate one and get the right answer.
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  3. #3
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    Re: Rearranging the GEH Statistical Equation

    GEH^2 = 2(M-C)^2/[M+C]
    GEH^2*[M+C} = 2(M-C)^2
    GEH^2*M + GEH^2*C = 2[M^2 - 2MC + C^2]
    M[GEH^2 + 4C] = 2M^2 + 2C^2
    where did the GEH^2*C go?
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  4. #4
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    Re: Rearranging the GEH Statistical Equation

    Yeah I forgot it (thanks for spotting it). So it should be:

    GEH^2*M + GEH^2*C = 2[M^2 - 2MC + C^2]
    M[GEH^2 + 4C] = 2M^2 + 2C^2 - GEH^2*C

    M = [2M^2 + 2C^2 - GEH^2*C]/[GEH^2 + 4C]
    = 2M^2/[GEH^2 + 4C] + [2C^2 - GEH^2*C]/[GEH^2 + 4C]

    Let a = 2/[GEH^2 + 4C] and c = [2C^2 - GEH^2*C]/[GEH^2 + 4C]

    So aM^2 - M + c = 0 with new a and c.
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