SOLUTION: the sum of a positive number and twice its square is 6.72. find the number

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Question 540514: the sum of a positive number and twice its square is 6.72. find the number
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
the sum of a positive number and twice its square is 6.72. find the number
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x + 2x^2 = 6.72
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B1x%2B-6.72+=+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=%281%29%5E2-4%2A2%2A-6.72=54.76.

Discriminant d=54.76 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+54.76+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+54.76+%29%29%2F2%5C2+=+1.6
x%5B2%5D+=+%28-%281%29-sqrt%28+54.76+%29%29%2F2%5C2+=+-2.1

Quadratic expression 2x%5E2%2B1x%2B-6.72 can be factored:
2x%5E2%2B1x%2B-6.72+=+%28x-1.6%29%2A%28x--2.1%29
Again, the answer is: 1.6, -2.1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B1%2Ax%2B-6.72+%29

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It's 1.6