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Popular >

t^2e^t+2te^t-8e^t=0

Solution

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

Solution

t = 2, t = - 4

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

If

ab = 0

then

a = 0

or

b = 0

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

Solve

e^{t} = 0 :

No Solution for

t \in R

Solve

t - 2 = 0 : t = 2

Solve

t + 4 = 0 : t = - 4

t = 2, t = - 4

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ln (\frac{8}{e ^{4 x}}) = 24

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e^{m x} (m^{2} + 6 m + 5) = 0

4^{8^{3+2x}}=2^{2^{7x-1}}

4^{8^{3 + 2 x}} = 2^{2^{7 x - 1}}

2 \cdot 3^{\frac{x}{5}} = 1

Frequently Asked Questions (FAQ)

What is the answer to t^2e^t+2te^t-8e^t=0 ?
The answer to t^2e^t+2te^t-8e^t=0 is t=2,t=-4