# Solving $y = xc^x + x + 1$, where c is a constant

How do you solve $xc^x + x + 1 = 0$ for $x$, where $c$ is a constant?

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Doesn't look like something you can solve neatly, or even use the Lambert function on... –  Ｊ. Ｍ. Oct 23 '11 at 8:41
small comment on existence..for sufficiently large negative values of $x$, $y$ is negative and for some positive values of $x$, $y$ is positive, since the function is continuous it seems to have a solution... –  Dinesh Oct 23 '11 at 8:41
@Dinesh: I think your statements require positive $c$. –  Henry Oct 23 '11 at 9:22
@Henry yes..I missed that. –  Dinesh Oct 23 '11 at 9:26
Title $\ne$ body. Do you want $y$ in there, or do you want zero? Please decide and edit accordingly. –  Gerry Myerson Oct 23 '11 at 11:35

If you need the root for particular $c$ (and $c\neq 0, 1$) you will need to approximate the root, for instance by plotting the function and looking for $x$-intercepts, or asking Wolfram Alpha. There also exist advanced numerical techniques, such as Newton's Method, that you could use to very accurately approximate roots of functions yourself.