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aktech/Solve by LambertW.md

Created March 4, 2015 19:30
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Solve by LambertW
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Solve by LambertW.md

This can be solved using properties of LambertW Function.

x + exp(x**2) = 0
1 = -x*exp(-x**2)
squarring both sides
1 = (x**2)*(exp(-2*x**2))
Multiply by -2 on both sides
-2 = (-2*x**2)*(exp(-2*x**2))
Taking LambertW on both sides:
LambertW(-2) = LambertW((-2*x**2)*(exp(-2*x**2)))
LambertW(-2) = -2*x**2
x = I*sqrt(LambertW(-2)/2)  # Answer!
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