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e^x+x equation

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Numerical solution:

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The solution

You have entered [src]
 x        
E  + x = 0
$$e^{x} + x = 0$$
The graph
Rapid solution [src]
x1 = -W(1)
$$x_{1} = - W\left(1\right)$$
x1 = -LambertW(1)
Sum and product of roots [src]
sum
-W(1)
$$- W\left(1\right)$$
=
-W(1)
$$- W\left(1\right)$$
product
-W(1)
$$- W\left(1\right)$$
=
-W(1)
$$- W\left(1\right)$$
-LambertW(1)
Numerical answer [src]
x1 = -0.567143290409784
x1 = -0.567143290409784