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Math Help - Make Y the subject

  1. #1
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    Make Y the subject

    2(y)^2 - 3y = x + 2
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  2. #2
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    Re: Make Y the subject

    You should recognize this as a Quadratic Equation and proceed. Completing the Square would be a nice, instructive method.
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  3. #3
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    Re: Make Y the subject

    Less instructive: use the quadratic formula to solve the equation 2y^2- 3y- (x+ 2)= 0/
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  4. #4
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    Re: Make Y the subject

    Less instructive yet(!): let k = x + 2; then: 2y^2 - 3y - k = 0
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  5. #5
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    Re: Make Y the subject

    2(Y)^2 - 3Y - K = 0 (K = X+2)

    Y^2 - (3/2)Y - K/2 = 0

    (Y - 3/4)(Y - 3/4) - K/2 - 9/16 = 0

    (Y - 3/4)^2 - (K/2 + 9/16) = 0

    (Y - 3/4)^2 = (K/2 + 9/16)

    Y - 3/4 = sqrt(K/2 + 9/16)

    Y = 3/4 + sqrt(K/2 + 9/16)

    Y = 3/4 + sqrt((X + 2)/2 + 9/16)

    Y = 3/4 + sqrt((8X + 16)/16 + 9/16)

    Y = 3/4 + sqrt((8X + 16 + 9)/16)

    Y = sqrt((8X + 25)/16)

    Y = (3 +/- sqrt(8X + 25))/4
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  6. #6
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    Re: Make Y the subject

    Quote Originally Posted by ajwright View Post
    2(Y)^2 - 3Y - K = 0 (K = X+2)

    Y^2 - (3/2)Y - K/2 = 0

    (Y - 3/4)(Y - 3/4) - K/2 - 9/16 = 0

    (Y - 3/4)^2 - (K/2 + 9/16) = 0

    (Y - 3/4)^2 = (K/2 + 9/16)

    Y - 3/4 = +/- sqrt(K/2 + 9/16)

    Y = 3/4 +/- sqrt(K/2 + 9/16)

    Y = 3/4 +/- sqrt((X + 2)/2 + 9/16)

    Y = 3/4 +/- sqrt((8X + 16)/16 + 9/16)

    Y = 3/4 +/- sqrt((8X + 16 + 9)/16)

    Y = 3/4 +/- sqrt((8X + 25)/16)

    Y = (3 +/- sqrt(8X + 25))/4
    You need to try very hard make sure every step of your working is correct. See the corrections in red. The final answer is correct though, well done.
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  7. #7
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    Re: Make Y the subject

    WHY do all that work? Never heard of the quadratic formula?

    2y^2 - 3y - k = 0 , where k = x + 2

    y = {-(-3) +/- SQRT[(-3)^2 - 4(2)(-k)]} / 4

    y = [3 +/- SQRT(9 + 8k)] / 4
    Substitute k = x + 2:
    y = [3 +/- SQRT(9 + 8(x + 2))] / 4

    y = [3 +/- SQRT(8x + 25)] / 4

    Done!
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