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Popular >

e^x+x-2=0

Solution

e^{x} + x - 2 = 0

Solution

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

+1

Decimal Notation

x = 0.44285 \dots

Solution steps

e^{x} + x - 2 = 0

Prepare

e^{x} + x - 2 = 0

for Lambert form:

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

Rewrite the equation with

- x + 2 = u

and

x = - u + 2

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

3^{1 - x} = 2

2^{4 x} = 16

2^{x} - 3^{x} - 3^{x} = 0

4 (10)^{x} = 20

2 e^{2 x + 7} - 15 = 0

Frequently Asked Questions (FAQ)

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