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Popular >

x+e^x=0,x

Solution

x + e^{x} = 0, x

Solution

x = - W_{0} (1)

+1

Decimal Notation

x = - 0.56714 \dots

Solution steps

x + e^{x} = 0

Prepare

x + e^{x} = 0

for Lambert form:

1 = - e^{- x} x

Rewrite the equation with

- x = u

and

x = - u

1 = - e^{u} (- u)

Rewrite

1 = - e^{u} (- u)

in Lambert form:

- e^{u} (- u) = 1

Solve

- e^{u} (- u) = 1 : u = W_{0} (1)

u = W_{0} (1)

Substitute back

u = - x,

solve for

x

Solve

- x = W_{0} (1) : x = - W_{0} (1)

x = - W_{0} (1)

Popular Examples

9 = 3^{x + 1}

\frac{1}{5} = 5^{2 c + 3}

3^{x-2}=5^{2x+1}

3^{x - 2} = 5^{2 x + 1}

6^{2x}-42(6^x)+216=0

6^{2 x} - 42 (6^{x}) + 216 = 0

solvefor y,e^{x^2y}=x+y solve for

y, e^{x^{2} y} = x + y

Frequently Asked Questions (FAQ)

What is the answer to x+e^x=0,x ?
The answer to x+e^x=0,x is x=-\W_{0}(1)