What is the answer to 64e^{8x}x^2+32e^{8x}x+2e^{8x}=0 ?

The answer to 64e^{8x}x^2+32e^{8x}x+2e^{8x}=0 is x=(-2+sqrt(2))/8 ,x=-(sqrt(2)+1)/(4sqrt(2))

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64e^{8x}x^2+32e^{8x}x+2e^{8x}=0

64 e^{8 x} x^{2} + 32 e^{8 x} x + 2 e^{8 x} = 0

x = \frac{- 2 + 2}{8}, x = - \frac{2 + 1}{4 2}

Decimal Notation

x = - 0.07322 \dots, x = - 0.42677 \dots

Solution steps

64 e^{8 x} x^{2} + 32 e^{8 x} x + 2 e^{8 x} = 0

Factor

2 e^{8 x} (32 x^{2} + 16 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{8 x} = 0 or 32 x^{2} + 16 x + 1 = 0

Solve

e^{8 x} = 0 :

No Solution for

x \in R

Solve

32 x^{2} + 16 x + 1 = 0 : x = \frac{- 2 + 2}{8}, x = - \frac{2 + 1}{4 2}

x = \frac{- 2 + 2}{8}, x = - \frac{2 + 1}{4 2}

2^{(7 - 3 x)} = \frac{1}{4}

2^{x + 5} - 3 \cdot 2^{x} = 29

5510 = 5000 (1 + 0.034)^{x}

4^{2 n} = 64

2^{x + 3} = 2^{x - 2} + 62

What is the answer to 64e^{8x}x^2+32e^{8x}x+2e^{8x}=0 ?
The answer to 64e^{8x}x^2+32e^{8x}x+2e^{8x}=0 is x=(-2+sqrt(2))/8 ,x=-(sqrt(2)+1)/(4sqrt(2))