Faldage's intensifier explanation makes a lot of sense, particularly since one of the definitions of "resolve" is "solve":

From Dictionary.com:

resolve

5. To find a solution to; solve. See Synonyms at solve.

This may sound like a stretch but there is a sense in which the number 1 definition of "resolve", namely, "To make a firm decision about" does mean to "solve again", Jackie.

When we "solve" a problem, we do not necessarily act on its implications.

"Solving" a problem gives us an intellectual understanding of a particular fact situation. It does not necessarily give us the "resolve" to act on that understanding.

When we take action on a problem we have solved, we take that which we have solved to a higher level. In this sense, we have 'redoubled' the solving. We have converted passive awareness into practical consequences.