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solve for X 30y=x^2-14x+13

  • Math -

    x^2 - 14 x + 13 = 30 y
    x^2 - 14 x = 30 y - 13
    x^2 - 14 x + 49 = 30 y + 36
    (x-7)^2 = 30 y + 36
    x - 7 = +/- sqrt (30 y + 36)
    x = 7 +/- sqrt (30 y + 36)

  • Math -

    This is so much harder than your other question that I suspect a typo by the way.

  • Math -

    x^2 - 14 x + 13 = 30 y
    x^2 - 14 x = 30 y - 13
    x^2 - 14 x + 49 = 30 y + 36 ****
    (x-7)^2 = 30 y + 36
    x - 7 = +/- sqrt (30 y + 36)
    x = 7 +/- sqrt (30 y + 36)

    where did you get the 49 or 36

  • Math -

    Completing the square
    x^2 + a x = something
    x^2 + a x + (a/2)^2 = something + (a/2)^2
    so
    if
    x^2 -14 x = something
    then
    x^2 - 14 x +(14/2)^2 = something + (14/2)^2
    or
    x^2 - 14 x + 49 = something + 49
    (x-7)^2 = something + 49
    x - 7 = +/- sqrt (something + 49)

    by taking half the second coefficient and squaring it, I get a perfect square.

  • Math -

    and 49 - 13 = 36

  • Math -

    why is this not correct

    30y = x^2 - 14x + 13
    - 13
    30y - 13 = x^2 - 14x
    _________ ___________
    -14 -14

    x = sqrt 30y-13
    _______
    -14

    Im really trying to follow your work... This is what I got the first time I tried before i asked...

  • Math -

    sorry the division signs didn't line up correctly

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