Finding small equation solutions with great precision with Solvesys and Longfloat

[math7]

Hi, I was playing with my HP 50g for a while, especially with the Solvesys application which I think is great, and also with the excellent library created long ago "longfloat" that allows you to choose the number of digits to work with extended integers. On the other hand I have noticed that for some equations whose solution are numbers like x = 1.1618E-16 neither Solvesys nor the application incorporated in the HP 50g can find these values as solutions. However, I have seen that in this extraordinary calculator you can do "almost everything" in terms of calculations, but there is some way to combine the Longfloat or similar library with Solvesys so that the calculator can work internally with more decimals and of the correct answer?
The following link refers to a type of these equations or systems.
https://www.hpmuseum.org/forum/thread-76...t=solvesys