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Popular >

(x+2)e^x=1

Solution

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

Solution

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

+1

Decimal Notation

x = - 0.44285 \dots

Solution steps

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

Rewrite the equation with

x + 2 = u

and

x = u - 2

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

Simplify

e^{u - 2} u = 1

Rewrite

e^{u - 2} u = 1

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

solvefor t,a(t)=a_{0}*e^{-0.025t}solve for

t, a (t) = a_{0} \cdot e^{- 0.025 t}

3(4^x)+4^{x-1}=52

3 (4^{x}) + 4^{x - 1} = 52

4^{2x}+12=2^{2x+3}

4^{2 x} + 12 = 2^{2 x + 3}

4^{3x}=32^{x-1}

4^{3 x} = 3 2^{x - 1}

25^{x-1}+100=5^{2x-1}

2 5^{x - 1} + 100 = 5^{2 x - 1}

Frequently Asked Questions (FAQ)

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