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

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

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

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

x = 0, x = 2

Solution steps

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

Factor

2 x e^{- x} + (- e^{- x}) x^{2} : e^{- x} x (2 - x)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

e^{- x} = 0 :

No Solution for

x \in R

Solve

2 - x = 0 : x = 2

x = 0, x = 2

1 0^{\frac{x}{3}} = 20

3^{x + 1} + 3^{x + 2} + 3^{x + 3} = 351

70 = 16 + 72 \cdot e^{- 175 t}

1 0^{3 x - 2} = 13

2 e^{2 x} = 1

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