# Converting a Mixed SUBSET-SUM Problem To All-Positive Case

Let’s say we have a SUBSET-SUM problem with list {$$x_1,x_2,x_3,…x_N$$} and weight $$W$$, with some of $$x_i<0$$. Is there a known way, in polynomial time, to convert this problem into an equivalent problem, but with all $$x_i \geq 0$$? And if there aren’t any, is it possible for there to be such an algorithm?