1/2 x^3 - x
factor out an x
x (1/2 x^2 - 1)
set each equal to zero so x = 0 is one solution
1/2 x^2 - 1 = 0
add 1 to both sides
1/2 x^2 = 1
multiply both sides by 2
x^2 = 2
square root both sides keeping in mind that you need both positive and negative
x = sqroot (2) and x = -sqroot (2)
final answers x = 0, sqroot (2), -sqroot(2)