Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?


share|cite|improve this question
up vote 2 down vote accepted

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

share|cite|improve this answer

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

$x = -W(-\frac{y}{e}) - 1$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.