Question

How do you solve for x in this equation? `e^{-\frac{x^2}{2}}x^2-e^{-\frac{x^2}{2}}=0`

`e^{-\frac{x^2}{2}}x^2-e^{-\frac{x^2}{2}}=0`

Answer 1

`x = +- 1`

Explanation:

Factor:

`e^(-x^2/2)(x^2 - 1) = 0`

`e^(-x^2/2)(x+ 1)(x- 1)=0`

The first equation has no solution (because `e^(-x^2)/2` never hits `0`).

Thus `x= +-1`.

Hopefully this helps!