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Popular >

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

Solution

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

Solution

x = 0, x = - 2

Solution steps

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

Subtract

2 x e^{- x}

from both sides

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

Simplify

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

Factor

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

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

Using the Zero Factor Principle:

If

ab = 0

then

a = 0

or

b = 0

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

Solve

e^{- x} = 0 :

No Solution for

x \in R

Solve

x + 2 = 0 : x = - 2

x = 0, x = - 2

Popular Examples

6^{2 x + 5} - 36 = 0

7(3^x)=3(5^{(5x-4)})

7 (3^{x}) = 3 (5^{(5 x - 4)})

4^{x+1}= 1/(8sqrt(2))

4^{x + 1} = \frac{1}{8 2}

5^{3 x + 4} = 45

2 \cdot 5^{x + 1} = 250

Frequently Asked Questions (FAQ)

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