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Popular >

x^2e^x-2xe^x-3e^x=0

Solution

x^{2} e^{x} - 2 x e^{x} - 3 e^{x} = 0

Solution

x = - 1, x = 3

Solution steps

x^{2} e^{x} - 2 x e^{x} - 3 e^{x} = 0

Factor

x^{2} e^{x} - 2 x e^{x} - 3 e^{x} : e^{x} (x + 1) (x - 3)

e^{x} (x + 1) (x - 3) = 0

Using the Zero Factor Principle:

If

ab = 0

then

a = 0

or

b = 0

e^{x} = 0 or x + 1 = 0 or x - 3 = 0

Solve

e^{x} = 0 :

No Solution for

x \in R

Solve

x + 1 = 0 : x = - 1

Solve

x - 3 = 0 : x = 3

x = - 1, x = 3

Popular Examples

(sqrt(2))^k=0.5

(2)^{k} = 0.5

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

10^{x^2+8x+1}=1

1 0^{x^{2} + 8 x + 1} = 1

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

3 2^{- 9 x + 9} = 16

Frequently Asked Questions (FAQ)

What is the answer to x^2e^x-2xe^x-3e^x=0 ?
The answer to x^2e^x-2xe^x-3e^x=0 is x=-1,x=3