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

  1. #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.

    Answer (derived from cad dimensions) : x = 506.53

    Here is as far as I could simplify :

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

  2. #2
    Elite Member
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    You cannot "solve" this one, either: [tex]x+2 = e^{x}[/tex]. There are Real Numbers solutions.

    Who told you to "Solve for x" and why do you believe it is possible?
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

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

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

    Follow that?
    I'm just an imagination of your figment !

  4. #4
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    Quote Originally Posted by nashbaker View Post
    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

    . . . . .[tex]x\, +\, 40\, =\, \left(\dfrac{x}{2}\right)\, \left(\dfrac{e^{-200}}{x}\right)\, +\, \left(\dfrac{x}{2}\right)\, \left(\dfrac{e^{200}}{x}\right) [/tex]

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

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

    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.
    Last edited by stapel; 12-05-2017 at 02:34 PM. Reason: Tweaking LaTeX.

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