Solving an equation on the HP50G (as compared to the Prime)

[Thomas Okken]

4.5006e-2 is not a solution, but it is a local minimum, which is why the numerical solver can converge there. The HP-42S solver does this, too, but it at least helpfully tells you "Extremum" when it does so.

With different starting values, you can guide it to the actual root. My copy of the HP-50g manual (edition 1, April 2006) has this example on page 6-10, and while it also fails to point out that 4.5006e-2 is an extremum and not a root, it does show how to enter a starting value of -3 to get the root -3.045.