What is the answer to 4e^{2x}x^2+8e^{2x}x+2e^{2x}=0 ?

The answer to 4e^{2x}x^2+8e^{2x}x+2e^{2x}=0 is x=(-2+sqrt(2))/2 ,x=-(sqrt(2)+1)/(sqrt(2))

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4e^{2x}x^2+8e^{2x}x+2e^{2x}=0

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

x = \frac{- 2 + 2}{2}, x = - \frac{2 + 1}{2}

Decimal Notation

x = - 0.29289 \dots, x = - 1.70710 \dots

Solution steps

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

Factor

2 e^{2 x} (2 x^{2} + 4 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{2 x} = 0 or 2 x^{2} + 4 x + 1 = 0

Solve

e^{2 x} = 0 :

No Solution for

x \in R

Solve

2 x^{2} + 4 x + 1 = 0 : x = \frac{- 2 + 2}{2}, x = - \frac{2 + 1}{2}

x = \frac{- 2 + 2}{2}, x = - \frac{2 + 1}{2}

y, e^{x y} = 4 y

1000 (1.03)^{t} = 5000

3^{2 x} - 28 \times 3^{x} + 27 = 0

1808 = 60 t + 1800 e^{- \frac{t}{30}}

2^{x} = 61

What is the answer to 4e^{2x}x^2+8e^{2x}x+2e^{2x}=0 ?
The answer to 4e^{2x}x^2+8e^{2x}x+2e^{2x}=0 is x=(-2+sqrt(2))/2 ,x=-(sqrt(2)+1)/(sqrt(2))