SOLUTION: Solve equation algebraically. 5e^x=10-e^-x

Question 644596: Solve equation algebraically. 5e^x=10-e^-x
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Solve equation algebraically. 5e^x=10-e^-x
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5e^x=10-e^-x

Multiply by e^x

Sub y for e^x

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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=80 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.89442719099992, 0.105572809000084. Here's your graph:

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e^x = 1 + sqrt(0.8)
x = ln(1+sqrt(0.8))
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e^x = 1 - sqrt(0.8)
x = ln(1-sqrt(0.8))
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Just calculator work left.
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