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

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Apr 28th 2011, 03:24 PM
scounged

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?
Apr 28th 2011, 03:27 PM
pickslides

There is no way to solve it algebraically. Your calculator has employed a numerical method to find an approximation
Apr 28th 2011, 03:39 PM
scounged

Hmmm. That's too bad really, but ah well...
Apr 28th 2011, 03:42 PM
pickslides

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'.
Apr 28th 2011, 08:59 PM
mr fantastic

Quote:

Originally Posted by scounged

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
May 1st 2011, 09:38 AM
scounged

After doing a little bit of research I see now that x=-(Omega constant), or x=-W(1)