What is the answer to 4x^2e^{-2x}-8xe^{-2x}+2e^{-2x}=0 ?

The answer to 4x^2e^{-2x}-8xe^{-2x}+2e^{-2x}=0 is x=(2+sqrt(2))/2 ,x=(2-sqrt(2))/2

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4x^2e^{-2x}-8xe^{-2x}+2e^{-2x}=0

4 x^{2} e^{- 2 x} - 8 x e^{- 2 x} + 2 e^{- 2 x} = 0

x = \frac{2 + 2}{2}, x = \frac{2 - 2}{2}

Decimal Notation

x = 1.70710 \dots, x = 0.29289 \dots

Solution steps

4 x^{2} e^{- 2 x} - 8 x e^{- 2 x} + 2 e^{- 2 x} = 0

Factor

2 e^{- 2 x} (2 x^{2} - 4 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{- 2 x} = 0 or 2 x^{2} - 4 x + 1 = 0

Solve

e^{- 2 x} = 0 :

No Solution for

x \in R

Solve

2 x^{2} - 4 x + 1 = 0 : x = \frac{2 + 2}{2}, x = \frac{2 - 2}{2}

x = \frac{2 + 2}{2}, x = \frac{2 - 2}{2}

4^{x + 1} - 2^{x + 1 + 2} = 0

x^{x} = \frac{2}{2}

25 6^{3 x + 3} = 102 4^{2 x + 2}

216 = 6^{2 r - 11}

2^{x - x^{2}} = \frac{1}{4 ^{x}}

What is the answer to 4x^2e^{-2x}-8xe^{-2x}+2e^{-2x}=0 ?
The answer to 4x^2e^{-2x}-8xe^{-2x}+2e^{-2x}=0 is x=(2+sqrt(2))/2 ,x=(2-sqrt(2))/2