  We refine the solvability of quadratic semimartingale BSDEs by employing a
Lipschitz-quadratic regularization procedure. In the first step, we prove an
existence and uniqueness result for a class of Lipschitz-quadratic BSDEs. A
corresponding stability theorem and a Lipschitz-quadratic regularization are
developed to solve quadratic BSDEs. The advantage of our approach is that much
weaker conditions ensure the existence and uniqueness results.
