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Popular >

2x+e^x=0

Solution

2 x + e^{x} = 0

Solution

x = - W_{0} (\frac{1}{2})

+1

Decimal Notation

x = - 0.35173 \dots

Solution steps

2 x + e^{x} = 0

Prepare

2 x + e^{x} = 0

for Lambert form:

1 = - 2 e^{- x} x

Rewrite the equation with

- x = u

and

x = - u

1 = - 2 e^{u} (- u)

Rewrite

1 = - 2 e^{u} (- u)

in Lambert form:

e^{u} u = \frac{1}{2}

Solve

e^{u} u = \frac{1}{2} : u = W_{0} (\frac{1}{2})

u = W_{0} (\frac{1}{2})

Substitute back

u = - x,

solve for

x

Solve

- x = W_{0} (\frac{1}{2}) : x = - W_{0} (\frac{1}{2})

x = - W_{0} (\frac{1}{2})

Popular Examples

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

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

128 = 2^{x}

e^{-x}+1/5 x-1=0

e^{- x} + \frac{1}{5} x - 1 = 0

(\frac{1}{3})^{x} = 243

4^{n} \cdot 4^{2} = 16384

Frequently Asked Questions (FAQ)

What is the answer to 2x+e^x=0 ?
The answer to 2x+e^x=0 is x=-\W_{0}(1/2)