First, the word "explaining" comes from a word that refers to "opening up the meaning" of the text of scripture. We could also say that Paul's intent was to hopefully "open the minds" of his hearers. Undoubtedly there had been much prayer invested in this endeavor, since much like preaching, apologetics will never succeed apart from the Holy Spirit's intervention.
Apologetics functions to prepare the mind and heart of the unbeliever for what will be the presentation of the Gospel. It may take only one apologetical encounter, or one may not even get through the whole presentation before the person says they're ready to believe. Again, the Holy Spirit is the One who brings people to point of certainty in saving faith (James 1:18; Hebrews 11:1).