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

The answer to x^2e^{2x}+2xe^{2x}=8e^{2x} is x=2,x=-4

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x^2e^{2x}+2xe^{2x}=8e^{2x}

x^{2} e^{2 x} + 2 x e^{2 x} = 8 e^{2 x}

x = 2, x = - 4

Solution steps

x^{2} e^{2 x} + 2 x e^{2 x} = 8 e^{2 x}

Subtract

8 e^{2 x}

from both sides

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

Simplify

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

Factor

x^{2} e^{2 x} + 2 x e^{2 x} - 8 e^{2 x} : e^{2 x} (x - 2) (x + 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

e^{2 x} = 0 :

No Solution for

x \in R

Solve

x - 2 = 0 : x = 2

Solve

x + 4 = 0 : x = - 4

x = 2, x = - 4

4^{2 x + 6} = 6 4^{2 x - 4}

5^{x} = 16

e^{x} + 15 e^{- x} - 8 = 0

3^{x - 9} = 8 1^{5 x + 1}

3^{1 - 2 x} = 243

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