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Popular >

e^x+2x=0

Solution

e^{x} + 2 x = 0

Solution

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

+1

Decimal Notation

x = - 0.35173 \dots

Solution steps

e^{x} + 2 x = 0

Prepare

e^{x} + 2 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

1.2 x = 1. 2^{x}

16^x+3*4^x-10=0

1 6^{x} + 3 \cdot 4^{x} - 10 = 0

2^{x} - 8 = 0

3^{2x}-5(3^x)=-6

3^{2 x} - 5 (3^{x}) = - 6

2^{x} = \frac{1}{3}

Frequently Asked Questions (FAQ)

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