  We prove that, for every integer $n \ge 2$, a finite or infinite countable
group $G$ can be embedded into a 2-generated group $H$ in such a way that the
solvability of quadratic equations of length at most $n$ is preserved, i.e.,
every quadratic equation over $G$ of length at most $n$ has a solution in $G$
if and only if this equation, considered as an equation over $H$, has a
solution in $H$.
