solving this for x (zero of the function)

I can't seem to figure out how to solve this for x without graphing it:

0=x^3-3x+1

Sometimes with cubics you can find one zero just by inspection and then the other two by synthetic division. Not so in this case. Is this problem in a section about approximating roots (i.e, Newton's method)?

Ideally we would start with the rational roots theorem but here the only possible zeroes are -1 and 1 neither of which are zeroes.

Graphically is the best way to go here. the cubic equation is rather long and involved but:

If interested see Solving Cubic Equations


I would agree it would be simpler to use Newton's Method