SOLUTION: 7e^x=12-e^-x Solve algebraically. The first (-) is subtraction and the last (-) is a negative x. Thanks in advance.

Question 1096243: 7e^x=12-e^-x
Solve algebraically. The first (-) is subtraction and the last (-) is a negative x. Thanks in advance.

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
7e^x=12-e^-x
------
multiply by e^x
7e^(2x) = 12e^x - 1
7e^(2x) - 12e^x + 1 = 0

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=116 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.62645211530493, 0.0878335989807852. Here's your graph:

=============
e^x =~ 1.6264
x = ln(1.6264)
-------------------
e^x =~ 0.0878
x = ln(0.0878)

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