SOLUTION: if a number is decreased by its square, the result is 2 over 9. find the number.

Question 36833: if a number is decreased by its square, the result is 2 over 9. find the number.

Answer by vidhyak(98) (Show Source): You can put this solution on YOUR website!
Let the number be x
and the square of the number be x^2

x- x^2 = 2/9
Multiply by 9 on both sides
9x- 9x^2 = 2
9x- 9x^2 - 2 = 0
-9x^2 +9x -2 = 0
Multiply by a -1 on both sides
9x^2 -9x +2 = 0
9x^2 -6x - 3x +2 = 0
3x(3x-2) -1(3x - 2) = 0
(3x -1 )(3x - 2) = 0
X = 1/3, 2/3

Verify the results
x - x^2
1/3 - (1/3)^2
1/3 - 1/9
3-1
----
9
= 2/9

x - x^2
2/3 - (2/3)^2
2/3 - 4/9
6-4
----
9
= 2/9
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