SOLUTION: 2e^x-2e^-x=5 2e^x-2/e^x=5 let e^x=y. 2y-2/y=5 2y^2-2=5y 2y^2-5y-2=0

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Question 526583: 2e^x-2e^-x=5
2e^x-2/e^x=5
let e^x=y.
2y-2/y=5
2y^2-2=5y
2y^2-5y-2=0

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2e^x-2e^-x=5
2e^x-2/e^x=5
let e^x=y.
2y-2/y=5
2y^2-2=5y
2y^2-5y-2=0
Good so far.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-5x%2B-2+=+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=%28-5%29%5E2-4%2A2%2A-2=41.

Discriminant d=41 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+41+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+41+%29%29%2F2%5C2+=+2.85078105935821
x%5B2%5D+=+%28-%28-5%29-sqrt%28+41+%29%29%2F2%5C2+=+-0.350781059358212

Quadratic expression 2x%5E2%2B-5x%2B-2 can be factored:
2x%5E2%2B-5x%2B-2+=+%28x-2.85078105935821%29%2A%28x--0.350781059358212%29
Again, the answer is: 2.85078105935821, -0.350781059358212. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-5%2Ax%2B-2+%29

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e^x = the solutions
x = ln of the positive solution
x =~ ln(2.85)
x =~ 1.04732