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Robots operating in the real world must be able to handle both discrete and continuous change. Many robot behaviors can be controlled through numeric parameters (called control variables), which affect the rate of the continuous change. Previous approaches capable of reasoning efficiently with control variables impose severe restrictions that limit the expressivity of the problems that can be solved. A broad class of robotic applications require, for example, convex quadratic constraints on state variables and control variables that are jointly constrained and that affect multiple state variables simultaneously. However, extensions to prior approaches are not straightforward, since these characteristics are non-linear and hard to scale. We introduce cqScotty, a heuristic forward search planner that solves these problems efficiently. While naive formulations of consistency checks are not convex and do not scale, cqScotty uses an efficient convex formulation, in the form of a Second Order Cone Program (SOCP), that is very fast to solve. We demonstrate the scalability of our approach on three new realistic domains.