I have the following equation:
$e^{-x}(1+x) = 0.935$
How can I solve for $x$ by hand? I remember I learned an easy way to solve it, which I forgot. Any help?
Thanks,
I have the following equation:
$e^{-x}(1+x) = 0.935$
How can I solve for $x$ by hand? I remember I learned an easy way to solve it, which I forgot. Any help?
Thanks,
Your equation is NOT solvable by any direct means. The solution can be expressed with the so called, Lambert-W function. Here is a numerical solution
As Alex R explains, this is solvable by application of the Lambert-W function:
So we have $e^{-x}(1 + x) = y$
Let $u = -(x + 1)$, then
$e^{1+u}(-u) = y$
Or equivalently
$e^1 e^u (-u) = y$
Meaning that $ue^u = -\frac{y}{e}$
Then Lambert-W gives $u = W(-\frac{y}{e})$
Reversing our substitution we find that
$x = -W(-\frac{y}{e}) - 1$