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Math Help - I don't know if there's a mathod for solving this.

  1. #1
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    I don't know if there's a mathod for solving this.

    I'm just wondering if there's a way to solve this equation algebraically:

    e^{x}+ x=0

    My calculator gives me that x is approximately -0.567.
    I suspect that if there's a way to solve this it probably has something to do with complex numbers, but I don't know as I haven't started using them yet.

    And btw, is there something wrong with Latex, or is it just my computer that is getting a little anxious over something?
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  2. #2
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    There is no way to solve it algebraically. Your calculator has employed a numerical method to find an approximation
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  3. #3
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    Hmmm. That's too bad really, but ah well...
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  4. #4
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    Never fear, you can solve it yourself using numerical methods. If you are interested research 'the bisection method' and if you know a little bit of calculus try 'newtons method'.
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  5. #5
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    Quote Originally Posted by scounged View Post
    I'm just wondering if there's a way to solve this equation algebraically:

    e^{x}+ x=0

    My calculator gives me that x is approximately -0.567.
    I suspect that if there's a way to solve this it probably has something to do with complex numbers, but I don't know as I haven't started using them yet.

    And btw, is there something wrong with Latex, or is it just my computer that is getting a little anxious over something?
    e^x + x = 0 \Rightarrow e^x = -x \Rightarrow -x e^{-x} = 1 \Rightarrow -x = W(1) \Rightarrow x = -W(1)

    where W(x) is the Lambert W-function:

    solve Exp[x] + x = 0 - Wolfram|Alpha
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  6. #6
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    After doing a little bit of research I see now that x=-(Omega constant), or x=-W(1)
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