Python component doing Newtons method?

I would like to create a Python component which will calculate the value of x by Newton's method:

http://en.wikipedia.org/wiki/Newton%27s_method

Basically here is what I want to do.

An example:

I input a value of 10, as x1 into function. Then:

F(x1) = x - ((x^2-612)/2*x) or if we for the x=10, we have:

F(x1) = 10 - ((10^2-612)/2*10) = 35.6

Then I want to compute the same function but for x = F(x1) which is in the upper case 36.6. Or in numbers:

F(x2) = 35.6 - ((35.6^2-612)/2*35.6) = 26.39550561

then:

F(x3) = 26.39550561 - ((26.39550561^2-612)/2*26.39550561) = 26.79063549

and so on for F(x4), F(x5)... up until (Fx100).

I already posted the same message in the "General Discussion" forums, and they told me Hoopsnake can do this. But I did not like it. It seems Python component could do this automatically. Or could it?

Thank you.