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late 14c., "to disperse, dissipate, loosen," from Latin solvere "to loosen, dissolve; untie, release, detach; depart; unlock; scatter; dismiss; accomplish, fulfill; explain; remove," from PIE *se-lu-, from reflexive pronoun *s(w)e- (see idiom) + root *leu- "to loosen, divide, cut apart" (see lose). The meaning "explain, answer" is attested from 1530s; for sense evolution, see solution. Mathematical use is attested from 1737. Related: Solved; solving.