TI83+. Math-> Solver. Why does it give different solutions?

Question

Not sure if anyone still uses this one.... Recall the keystrokes:
Math 0:Solver Up arrow Enter equation Press ENTER

You will now be at a prompt displaying the equation, and a line saying x=### (prior solution) and a line below saying bound=

Then you type Alpha->ENTER (solve) I am getting different answers based on what is already entered in the x=__ line

Did anyone else look into why this is? What is the calculator doing? Is there an accepted way to get the "right" root? Do you clear the x=__ first?

Answer 1

If I recall correctly, it finds the solution nearest to what is already in the x= line. I think the calculator is using some sort of numerical method, and what you enter in x= is the initial guess for the algorithm.

Answer 2

I have a TI-84 Plus, which works basically in the same way. It doesn't simply apply a formula to resolve the equation, but actually builds up closer approximations from a guess. This is also why it can't give precise values such as $\sqrt 2$, the way simpler non-graphical calculators can.