SOLUTION: e^x+e^-x=7 I need to solve the exponential equation please help me get started.

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Question 188046: e^x+e^-x=7 I need to solve the exponential equation please help me get started.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
e%5Ex%2Be%5E%28-x%29=7 Start with the given equation


e%5Ex%2B1%2Fe%5Ex=7 Rewrite e%5E%28-x%29 as 1%2Fe%5Ex


Now let u=e%5Ex


u%2B1%2Fu=7 Replace each term e%5Ex with "u"


u%5E2%2B1=7u Multiply EVERY term by the LCD "u" to clear the fractions.


u%5E2-7u%2B1=0 Subtract 7u from both sides.


Now use the quadratic equation to solve for "u". Once you have the solutions in terms of "u", substitute u=e%5Ex back in to solve for "x".