Printable View
I'm just wondering if there's a way to solve this equation algebraically:
$\displaystyle e^{x}$+$\displaystyle x=0$
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?
There is no way to solve it algebraically. Your calculator has employed a numerical method to find an approximation
Hmmm. That's too bad really, but ah well...
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'.
$\displaystyle e^x + x = 0 \Rightarrow e^x = -x \Rightarrow -x e^{-x} = 1 \Rightarrow -x = W(1) \Rightarrow x = -W(1)$Quote:
Originally Posted by scounged
where W(x) is the Lambert W-function:
solve Exp[x] + x = 0 - Wolfram|Alpha
After doing a little bit of research I see now that x=-(Omega constant), or x=-W(1)
