SOLUTION: 1/x+1/(x+6)=1/5

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Question 877144: 1/x+1/(x+6)=1/5
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1/x+1/(x+6)=1/5
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1%2Fx%2B1%2F%28x%2B6%29=1%2F5
Multiply thru by 5x*(x+6) to eliminate fractions
5(x+6) + 5x = x(x+6)
5x+%2B+30+%2B+5x+=+x%5E2+%2B+6x
x%5E2+-+4x+-+30+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B-30+=+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=%28-4%29%5E2-4%2A1%2A-30=136.

Discriminant d=136 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+136+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+136+%29%29%2F2%5C1+=+7.8309518948453
x%5B2%5D+=+%28-%28-4%29-sqrt%28+136+%29%29%2F2%5C1+=+-3.8309518948453

Quadratic expression 1x%5E2%2B-4x%2B-30 can be factored:
1x%5E2%2B-4x%2B-30+=+%28x-7.8309518948453%29%2A%28x--3.8309518948453%29
Again, the answer is: 7.8309518948453, -3.8309518948453. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-30+%29