We develop a toolkit to decide some quadratic equations with constants
in certain self-similar groups and determine conditions under which
these tools work. It turns out that for explicitly given groups the
question of solvability of some equations reduces to a large but finite
number of calculations. For special cases we provide the algorithms in
the GAP language and use the computed results to verify that for example
the Gupta-Sidki has commutator width at most 3.