Question

solve x + ln x + e^x=0

Answer 1

you can solve it graphically or you can use Newton's method:
1) guess an answer (say x = 1)
2) update x by x := x - f(x) / (df/dx)
3) if f(x) is not small enough (say 10^-6) return to 2
x f(x) df/dx new x
1.000000 3.718282 4.718282 0.211942
0.211942 -0.103428 6.954357 0.226814
0.226814 -0.002215 6.663497 0.227146
0.227146 -0.000001 6.657462 0.227146
answer = 0.227146