Use Newton's method to approximate the root of the equation x^3+x+2=0 with initial guess x1=-1 gives:

Answer 1

Using trig get:

Xn+1 = Xn - Yn/Y'n
where
Y = x^3 + x + 2
Y' = 3x^2 + 1
for x = -1
Y = -1-1+2 = 0 well how embarrassing, we guessed it exactly
Y' = 4 irrelevant