What is the answer to solvefor x,be^{-2x}+3y+3x+11=0 ?

The answer to solvefor x,be^{-2x}+3y+3x+11=0 is x=(3\W(-(2b)/(3e^{\frac{-6y-22)/3)})-6y-22}{6}

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solvefor x,be^{-2x}+3y+3x+11=0

solve for

x, b e^{- 2 x} + 3 y + 3 x + 11 = 0

x = \frac{3 W ( - \frac{2 b}{3 e ^{\frac{- 6 y - 22}{3}}} ) - 6 y - 22}{6}

Solution steps

b e^{- 2 x} + 3 y + 3 x + 11 = 0

Prepare

b e^{- 2 x} + 3 y + 3 x + 11 = 0

for Lambert form:

b = (- 3 x - 3 y - 11) e^{2 x}

Rewrite the equation with

2 x + 2 y + \frac{22}{3} = u

and

x = \frac{3 u - 6 y - 22}{6}

b = (- 3 \frac{3 u - 6 y - 22}{6} - 3 y - 11) e^{2 \frac{3 u - 6 y - 22}{6}}

Simplify

b = e^{\frac{3 u - 6 y - 22}{3}} (- \frac{3 u - 6 y - 22}{2} - 3 y - 11)

Rewrite

b = e^{\frac{3 u - 6 y - 22}{3}} (- \frac{3 u - 6 y - 22}{2} - 3 y - 11)

in Lambert form:

e^{u} u = - \frac{2 b}{3 e ^{\frac{- 6 y - 22}{3}}}

Solve

e^{u} u = - \frac{2 b}{3 e ^{\frac{- 6 y - 22}{3}}} : u = W (- \frac{2 b}{3 e ^{\frac{- 6 y - 22}{3}}})

u = W (- \frac{2 b}{3 e ^{\frac{- 6 y - 22}{3}}})

Substitute back

u = 2 x + 2 y + \frac{22}{3},

solve for

x

Solve

2 x + 2 y + \frac{22}{3} = W (- \frac{2 b}{3 e ^{\frac{- 6 y - 22}{3}}}) : x = \frac{3 W ( - \frac{2 b}{3 e ^{\frac{- 6 y - 22}{3}}} ) - 6 y - 22}{6}

x = \frac{3 W ( - \frac{2 b}{3 e ^{\frac{- 6 y - 22}{3}}} ) - 6 y - 22}{6}

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

e^{x} = 5275

50 = 40 - 80 e^{(- 0.2 t)}

2^{(- x + 3)} = 64

e^{t} = - 1

What is the answer to solvefor x,be^{-2x}+3y+3x+11=0 ?
The answer to solvefor x,be^{-2x}+3y+3x+11=0 is x=(3\W(-(2b)/(3e^{\frac{-6y-22)/3)})-6y-22}{6}