SOLUTION: a number minus the ^2 of the number = 2/9

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Question 431405: a number minus the ^2 of the number = 2/9
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
a number minus the ^2 of the number = 2/9
.
Let x = the number
then
(in our case 1x%5E2%2B-1x%2B0.222222222222222+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A1%2A0.222222222222222=0.111111111111112.

Discriminant d=0.111111111111112 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+0.111111111111112+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+0.111111111111112+%29%29%2F2%5C1+=+0.666666666666667
x%5B2%5D+=+%28-%28-1%29-sqrt%28+0.111111111111112+%29%29%2F2%5C1+=+0.333333333333333

Quadratic expression 1x%5E2%2B-1x%2B0.222222222222222 can be factored:
1x%5E2%2B-1x%2B0.222222222222222+=+1%28x-0.666666666666667%29%2A%28x-0.333333333333333%29
Again, the answer is: 0.666666666666667, 0.333333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B0.222222222222222+%29