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Popular >

x=e^{-x}-2

Solution

x = e^{- x} - 2

Solution

x = W_{0} (e^{2}) - 2

+1

Decimal Notation

x = - 0.44285 \dots

Solution steps

x = e^{- x} - 2

Prepare

x = e^{- x} - 2

for Lambert form:

1 = (x + 2) e^{x}

Rewrite the equation with

x + 2 = u

and

x = u - 2

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

Simplify

1 = e^{u - 2} u

Rewrite

1 = e^{u - 2} u

in Lambert form:

e^{u} u = e^{2}

Solve

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

u = W_{0} (e^{2})

Substitute back

u = x + 2,

solve for

x

Solve

x + 2 = W_{0} (e^{2}) : x = W_{0} (e^{2}) - 2

x = W_{0} (e^{2}) - 2

Popular Examples

7^{3 x - 2} = 1

(2 e^{3 x})^{3} = 9

2^{2x}-2^{x+2}=32

2^{2 x} - 2^{x + 2} = 32

solvefor t,7A-2X+4B^t+3C=0 solve for

t, 7 A - 2 X + 4 B^{t} + 3 C = 0

5 = 4 + x + e^{x}

Frequently Asked Questions (FAQ)

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