What is the answer to e^{-x^2}-2e^{-x^2}x^2=0 ?

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

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

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

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

Decimal Notation

x = - 0.70710 \dots, x = 0.70710 \dots

Solution steps

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

Factor

e^{- x^{2}} - 2 e^{- x^{2}} x^{2} : - e^{- x^{2}} (2 x + 1) (2 x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

No Solution for

x \in R

Solve

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

Solve

2 x - 1 = 0 : x = \frac{1}{2}

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

e^{- 6 x} = 0.15

x^{l n (x)} = e^{(l n (x))^{3}}

e^{7 + 2 x} = 3

4 (2^{t}) = 10

e^{y} = 4

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