What is the answer to e^{-x}x^2-4e^{-x}x+2e^{-x}=0 ?

The answer to e^{-x}x^2-4e^{-x}x+2e^{-x}=0 is x=2+sqrt(2),x=2-sqrt(2)

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e^{-x}x^2-4e^{-x}x+2e^{-x}=0

e^{- x} x^{2} - 4 e^{- x} x + 2 e^{- x} = 0

x = 2 + 2, x = 2 - 2

Decimal Notation

x = 3.41421 \dots, x = 0.58578 \dots

Solution steps

e^{- x} x^{2} - 4 e^{- x} x + 2 e^{- x} = 0

Factor

e^{- x} (x^{2} - 4 x + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{- x} = 0 or x^{2} - 4 x + 2 = 0

Solve

e^{- x} = 0 :

No Solution for

x \in R

Solve

x^{2} - 4 x + 2 = 0 : x = 2 + 2, x = 2 - 2

x = 2 + 2, x = 2 - 2

x, e^{9 x} = 7 e^{- x}

6^{x - 5} = 7

2 x^{2} e^{- x} = 18 e^{- x}

25 (5^{2 x}) + 99 (5^{x}) - 4 = 0

2^{2 x} + 2 x - 6 = 0

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