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Popular >

5+e^x=-x/2+2

Solution

5 + e^{x} = - \frac{x}{2} + 2

Solution

x = - W_{0} (\frac{2}{e ^{6}}) - 6

+1

Decimal Notation

x = - 6.00493 \dots

Solution steps

5 + e^{x} = - \frac{x}{2} + 2

Prepare

5 + e^{x} = - \frac{x}{2} + 2

for Lambert form:

2 = (- x - 6) e^{- x}

Rewrite the equation with

- x - 6 = u

and

x = - u - 6

2 = (- (- u - 6) - 6) e^{- (- u - 6)}

Simplify

2 = e^{u + 6} u

Rewrite

2 = e^{u + 6} u

in Lambert form:

e^{u} u = \frac{2}{e ^{6}}

Solve

e^{u} u = \frac{2}{e ^{6}} : u = W_{0} (\frac{2}{e ^{6}})

u = W_{0} (\frac{2}{e ^{6}})

Substitute back

u = - x - 6,

solve for

x

Solve

- x - 6 = W_{0} (\frac{2}{e ^{6}}) : x = - W_{0} (\frac{2}{e ^{6}}) - 6

x = - W_{0} (\frac{2}{e ^{6}}) - 6

Popular Examples

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1 6^{2 x} = \frac{1}{8}

125 - 5^{2 x} = 0

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

Frequently Asked Questions (FAQ)

What is the answer to 5+e^x=-x/2+2 ?
The answer to 5+e^x=-x/2+2 is x=-\W_{0}(2/(e^6))-6