What is the answer to e^xx^2+4e^xx+2e^x=0 ?

The answer to e^xx^2+4e^xx+2e^x=0 is x=-2+sqrt(2),x=-2-sqrt(2)

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e^xx^2+4e^xx+2e^x=0

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

x = - 2 + 2, x = - 2 - 2

Solution steps

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

Factor

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

e^{x} = 0 :

No Solution for

x \in R

Solve

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

x = - 2 + 2, x = - 2 - 2

3^{2 x} = 9^{\frac{5}{2} x - 3}

x, 8 1^{x} = 3

2 e^{4 x - 2} = 9

10000 = 5000 (1 + 7.5)^{n}

5^{x - 1} = 5^{7 - 3 x}

What is the answer to e^xx^2+4e^xx+2e^x=0 ?
The answer to e^xx^2+4e^xx+2e^x=0 is x=-2+sqrt(2),x=-2-sqrt(2)