# What is the quadratic formula of #e^(2x) - 2e^x = 1#?

##### 1 Answer

Oct 31, 2015

#### Answer:

Recognise this as quadratic in

#x = ln(1+sqrt(2))#

#### Explanation:

This is an equation that is quadratic in

#(e^x)^2-2(e^x)-1 = 0#

If we substitute

#t^2-2t-1 = 0#

which is in the form

This has roots given by the quadratic formula:

#t = (-b+-sqrt(b^2-4ac))/(2a) = (2+-sqrt(4+4))/2 = 1+-sqrt(2)#

Now

So