All 4 Uses of

resolve
in
A Christmas Carol, by Charles Dickens

Every time he resolved within himself, after mature inquiry, that it was all a dream, his mind flew back again, like a strong spring released, to its first position, and presented the same problem to be worked all through, "Was it a dream or not?"
p. 30.7

resolved = decided

But scorning rest, upon his reappearance, he instantly began again, though there were no dancers yet, as if the other fiddler had been carried home, exhausted, on a shutter, and he were a bran-new man resolved to beat him out of sight, or perish.
p. 45.2 *

resolved = determined (having firm purpose)

But nothing doubting that to whomsoever they applied they had some latent moral for his own improvement, he resolved to treasure up every word he heard, and everything he saw; and especially to observe the shadow of himself when it appeared.
p. 97.8 *

resolved = decided

Definitions:

(1) (resolve as in: I resolved to stop drinking.)
to decide -- typically a firm or formal decision

In modern writing resolve is typically used to emphasize a firm or formal decision. In classic literature, it is used more frequently and often simply replaces decide or determine.
(2) (resolve as in: This committee hereby resolves...)
make a decision or voice an opinion by formal group vote
(3) (resolve as in: Her resolve weakened.)
firmness of purpose (strong determination to do something)
(4) (resolve as in: How was the problem resolved?)
to solve a problem, settle a disagreement, or for a situation to change
(5) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

Less commonly, resolve can mean:
- to make clearly visible -- as in "The microscope cannot resolve that level of detail."
- to divide into parts -- as in "The problem resolves into three parts,"or (math) "Resolve the polynomial into factors," or (chemistry) "As the temperature changes, the compound resolves into its component parts," or (physics) "The force on the inclined plane resolves into horizontal and vertical components."
- reduce or convert into something else -- as in "The URL is resolved to an IP address," or (music) "The progression is resolved as the dissonance is replaced by consonance."