What is the answer to x^2*e^x+x*e^x-e^x=0 ?

The answer to x^2*e^x+x*e^x-e^x=0 is x=(-1+sqrt(5))/2 ,x=(-1-sqrt(5))/2

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x^2e^x+xe^x-e^x=0

x^{2} \cdot e^{x} + x \cdot e^{x} - e^{x} = 0

x = \frac{- 1 + 5}{2}, x = \frac{- 1 - 5}{2}

Decimal Notation

x = 0.61803 \dots, x = - 1.61803 \dots

Solution steps

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

Factor

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

e^{x} = 0 :

No Solution for

x \in R

Solve

x^{2} + x - 1 = 0 : x = \frac{- 1 + 5}{2}, x = \frac{- 1 - 5}{2}

x = \frac{- 1 + 5}{2}, x = \frac{- 1 - 5}{2}

2^{3 x + 3} = 2^{3 x + 1} + 48

4^{2 x} + 2 0^{x} = 5^{2 x}

(1 2^{x})^{2} + 5 x - 4 = 1 2^{2} x + 6

(5^{k})^{2} = \frac{12 5 ^{3}}{( 5 ^{2} )}

2^{2 x + 6 x} - 16 = 0

What is the answer to x^2*e^x+x*e^x-e^x=0 ?
The answer to x^2*e^x+x*e^x-e^x=0 is x=(-1+sqrt(5))/2 ,x=(-1-sqrt(5))/2