This article considers the general mixed integer, quadratically constrained problem in combinatorial optimization and proposes a novel reformulation of the problem into an equivalent quadratic problem with a convex continuous relaxation. The article begins with an overview of the literature and the mathematical formulation of the problem, followed by the presentation of a family of equivalent formulations. This is followed by a method for calculating the best convex equivalent formulation which is then used to find the optimal solution to the problem. The fourth and fifth sections present an extension of the method to the case of equality constraints and the case where some of the variables are continuous, respectively. A large number of computational results are presented where the method is applied to numerous quadratic problems and the performance of the approach is evaluated.