What is the answer to 5-0.5x+5e^{-x}=0 ?

The answer to 5-0.5x+5e^{-x}=0 is x=\W_{0}(5/(0.5e^{10)})+5/(0.5)

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5-0.5x+5e^{-x}=0

5 - 0.5 x + 5 e^{- x} = 0

x = W_{0} (\frac{5}{0.5 e ^{10}}) + \frac{5}{0.5}

Decimal Notation

x = 10.00045 \dots

Solution steps

5 - 0.5 x + 5 e^{- x} = 0

Prepare

5 - 0.5 x + 5 e^{- x} = 0

for Lambert form:

5 = (0.5 x - 5) e^{x}

Rewrite the equation with

x - \frac{5}{0.5} = u

and

x = u + 10

5 = (0.5 (u + 10) - 5) e^{(u + 10)}

Simplify

5 = 0.5 e^{u + 10} u

Rewrite

5 = 0.5 e^{u + 10} u

in Lambert form:

e^{u} u = \frac{5}{0.5 e ^{10}}

Solve

e^{u} u = \frac{5}{0.5 e ^{10}} : u = W_{0} (\frac{5}{0.5 e ^{10}})

u = W_{0} (\frac{5}{0.5 e ^{10}})

Substitute back

u = x - \frac{5}{0.5},

solve for

x

Solve

x - \frac{5}{0.5} = W_{0} (\frac{5}{0.5 e ^{10}}) : x = W_{0} (\frac{5}{0.5 e ^{10}}) + \frac{5}{0.5}

x = W_{0} (\frac{5}{0.5 e ^{10}}) + \frac{5}{0.5}

3^{- x} = 0

e^{x} = 3.3

\frac{1 0 ^{6}}{1 0 ^{5}} = 1 0^{x}

9^{x + 10} + 22 = 100

2^{p + 3} = 67

What is the answer to 5-0.5x+5e^{-x}=0 ?
The answer to 5-0.5x+5e^{-x}=0 is x=\W_{0}(5/(0.5e^{10)})+5/(0.5)