# Thread: simplify x + 40 = (x/2)(e^-200/x) + (x/2)(e^200/x), and solve

1. ## simplify x + 40 = (x/2)(e^-200/x) + (x/2)(e^200/x), and solve

All,

I cannot figure out how to show all steps to the following problem.

Original equation: x + 40 = (x/2)(e^-200/x) + (x/2)(e^200/x)

Solve for x.

Here is as far as I could simplify :

x + 40 = (x/2)(e^(-200/x)) + (x/2)(e^(200/x))

2. You cannot "solve" this one, either: $x+2 = e^{x}$. There are Real Numbers solutions.

Who told you to "Solve for x" and why do you believe it is possible?

3. Originally Posted by nashbaker
x + 40 = (x/2)(e^-200/x) + (x/2)(e^200/x)
Let k = e^200

(x + 40)/(x/2) = 1/(kx) + k/x

4. Originally Posted by nashbaker
Original equation: x + 40 = (x/2)(e^-200/x) + (x/2)(e^200/x)

Here is as far as I could simplify :
x + 40 = (x/2)(e^(-200/x)) + (x/2)(e^(200/x))
Presumably it is the second of these that represents what you intended (though you didn't simplify anything); Denis took the first one, which means

. . . . .$x\, +\, 40\, =\, \left(\dfrac{x}{2}\right)\, \left(\dfrac{e^{-200}}{x}\right)\, +\, \left(\dfrac{x}{2}\right)\, \left(\dfrac{e^{200}}{x}\right)$

and which could be solved algebraically (but is too trivial to be what you meant); the second is

. . . . .$x\, +\, 40\, =\, \left(\dfrac{x}{2}\right)\, \left(e^{\frac{-200}{x}}\right)\, +\, \left(\dfrac{x}{2}\right)\, \left(e^{\frac{200}{x}}\right)$

and can only be solved by numerical approximation methods (which a CAD program will use). Wolfram Alpha gives the solution you provided, for this version.

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