resolute

Resolute comes from Latin resolutus, "released," the past participle of resolvō, "to release, to unbind" (re- + solvō, the root that also gives us solve).

The facts at hand don't trace how a word meaning 'released' came to describe firmness of purpose — only that this is its Latin root.

It shares its root solvō with English solve, both descending from the same Latin verb of loosening or releasing.