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Constraints involving Boolean and numerical variables are used widely, but it is difficult to solve especially when they contain nonlinear numerical expressions. Many existing methods for solving such constraints are incomplete. A new method is presented in this paper to solve Boolean combinations of nonlinear numerical constraints completely. This method transforms the nonlinear constraints into a special-formed optimization problem to solve them. A prototype tool is implemented, and somedoi:10.1360/jos160659 fatcat:woi5fm6ojze4hj7zlj7al35cfe