late 14c., "melt, dissolve, reduce to liquid;" intransitive sense from c.1400; from Old French resolver or directly from Latin resolvere "to loosen, loose, unyoke, undo; explain; relax; set free; make void, dispel," from re-, perhaps intensive, or "back" (see re-), + solvere "loosen" (see solve). Early 15c. as "separate into components," hence the use in optics (1785). Meaning "determine, decide upon" is from 1520s, hence "pass a resolution" (1580s). For sense evolution, compare resolute, adj.. Related: Resolved; resolving.

"determination, firmness or fixedness of purpose; a determination," 1590s, from resolve, v..