Use Newton's method to approximate a root of the equation $\displaystyle {x}^{{3}}-{2}{x}+{2}={0}$ as follows.

Let $\displaystyle {x}_{{0}}={0}$ be the initial approximation.
$\displaystyle {x}_{{1}}=$
(Find the actual numerical value.)

$\displaystyle {x}_{{2}}=$
(Find the actual numerical value.)

$\displaystyle {x}_{{3}}=$
(Find the actual numerical value.)
This is a great time to check your work and "submit".


It seems like our initial guess isn't so good. Use some other starting value.
Continue Newton's Method on your calculator until the value no longer changes.

$\displaystyle {x}_{{0}}=$ (Enter your starting guess here.)

$\displaystyle {x}\approx$ (Enter your final approximation for the zero.)