What is the answer to e^{-x}x^2+2e^{-x}x-e^{-x}=0 ?

The answer to e^{-x}x^2+2e^{-x}x-e^{-x}=0 is x=-1+sqrt(2),x=-1-sqrt(2)

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

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

x = - 1 + 2, x = - 1 - 2

Decimal Notation

x = 0.41421 \dots, x = - 2.41421 \dots

Solution steps

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

Factor

e^{- x} (x^{2} + 2 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{- x} = 0 or x^{2} + 2 x - 1 = 0

Solve

e^{- x} = 0 :

No Solution for

x \in R

Solve

x^{2} + 2 x - 1 = 0 : x = - 1 + 2, x = - 1 - 2

x = - 1 + 2, x = - 1 - 2

(\frac{1}{8})^{x - 3} = 1 6^{4 x - 3}

2^{k - 2} \cdot 5^{k - 2} = 100

5^{x + 5} = 7

5 \cdot 2^{x} = 1 0^{x}

e^{4 t} = 60

What is the answer to e^{-x}x^2+2e^{-x}x-e^{-x}=0 ?
The answer to e^{-x}x^2+2e^{-x}x-e^{-x}=0 is x=-1+sqrt(2),x=-1-sqrt(2)