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Popular >

e^{2x}=-x+2

Solution

e^{2 x} = - x + 2

Solution

x = - \frac{W _{0} ( 2 e ^{4} ) - 4}{2}

+1

Decimal Notation

x = 0.27314 \dots

Solution steps

e^{2 x} = - x + 2

Prepare

e^{2 x} = - x + 2

for Lambert form:

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

Rewrite the equation with

- 2 x + 4 = u

and

x = - \frac{u - 4}{2}

1 = (- (- \frac{u - 4}{2}) + 2) e^{- 2 (- \frac{u - 4}{2})}

Simplify

1 = e^{u - 4} (\frac{u - 4}{2} + 2)

Rewrite

1 = e^{u - 4} (\frac{u - 4}{2} + 2)

in Lambert form:

e^{u} u = 2 e^{4}

Solve

e^{u} u = 2 e^{4} : u = W_{0} (2 e^{4})

u = W_{0} (2 e^{4})

Substitute back

u = - 2 x + 4,

solve for

x

Solve

- 2 x + 4 = W_{0} (2 e^{4}) : x = - \frac{W _{0} ( 2 e ^{4} ) - 4}{2}

x = - \frac{W _{0} ( 2 e ^{4} ) - 4}{2}

Popular Examples

7^{3 x - 5} = 49

e^{2 x} = 4 e^{x} - 4

93 = 1 5^{x}

3^{x+1}+2(3^{x-1})=8

3^{x + 1} + 2 (3^{x - 1}) = 8

3^{2x}+2=3^{x+1}

3^{2 x} + 2 = 3^{x + 1}

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}=-x+2 ?
The answer to e^{2x}=-x+2 is x=-(\W_{0}(2e^4)-4)/2