TI-30X Pro MathPrint - How does num-solve work?

[wb.c]

So here is an example of Newton's Method of approximation for a starting value of 10.83.
As previously tabulated, the result should be 7.9772, and it indeed is.
The path to that answer is just wild!

   

This really shows how important the initial guess is for more complicated equations. Having an idea of what the function looks like and then using a table to isolate sign changes is really important.

For comparison, the Casio fx-991ex (latest edition) has these results.
x0= >10.84 : Cannot Solve
x0= >10.8 : Cannot Solve
x0= >10.83 : x=3.62

Makes me wonder which approximation method the Casio is using.