Question 608098: Greetings mathematic overlords,
My conundrum is as follows, I have this equation I am using to calculate a few values:
2x-(x/10)^2=y, from 0 to 100
Now this equation isn’t especially difficult and I get plenty of values out of it, such as when x=36 y=59.04, when x=20 y=26, when x=100 y=100, plotting a nice curve.
My issue now is that I need a way to somehow reverse this formula, so that when I know ‘y’ but not ‘x’ I can find ‘x’. I’ve spent a good hour now trying to come up with any tangible way to calculate ‘x’ by only knowing ‘y’ but it is simply beyond my abilities.
If it’s not too much trouble would you be able to help me find the formula to find ‘x’ from only ‘y’ so that all answers tie in with the equation 2x-(x/10)^2=y?
If possible it would be a great help to me if you were able to explain just how to come to determine such a formula so that I can work it out for myself in the future for similar equations.
Thank you for your time.
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! 2x - x^2 / 100 = y
200x - x^2 = 100y ___ x^2 - 200x = -100y
completing the square ___ x^2 - 200x + 10000 = 10000 - 100y
(x - 100)^2 = 100(100-y)
taking square root ___ x - 100 = ± 10 √(100-y) ___ x = 100 ± 10 √(100-y)
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