What works did the household of Cornelius do to be justified? None (Acts 10:43-46).
What work did they do that can show they are really the children of God and thus be saved on the Day of Wrath? Baptism (Acts 10:47-48 NASB).
In Peter's sermon to the Gentile household Peter said "
But in every nation he that feareth him, and worketh righteousness, is accepted with him." So there must be 'working righteousness" on the part of Cornelius to be aceepted with God.
We also know Cornelius was told to "believe" (
not told to believe only) Acts 10:43 and we know they were also water baptized, Acts 10:47,48.
We also know Cornelius would be saved by "words" (gospel message) Peter would preach to him Acts 11:14 Repentance and confession are both part of the gospel, Lk 13:3,5; Acts 2:38; Mt 10:32,33; Rom 10:9,10.
Jn 8:24-----------believing>>>>>>>>>>>>saves
Acts 2:38---------repentance>>>>>>>>>>saves
Rom 10:9,10----confession>>>>>>>>>>saves
1 Pet 3:21-------baptism>>>>>>>>>>>>saves
Since there is just one way to be saved, then believing
must include repentance, confession and baptism. Believing is sometimes used as a synecdoche (part stands for the whole) where believing includes repentance, confession and baptism. So even though repentance nor confession are specifically mentioned in Acts 10, "believe" in Acts 10:43 would include them, not exclude them. Just as when Peter said in 1 Pet 3:21 that baptism now saves us. Peter is
NOT saying "baptism ALONE" saves us, but baptism is used as a synecdoche were it includes believing, repenting and confession. Just as those who are said to have 'believed' in Acts 2:44 are the ones that were baptized in Acts 2:41 so we have the word "believed" in Acts 2:44 include being baptized.
Lastly in Acts 15 the apostles met in Jerusalem to discuss the issue of circumcision for there were some false teachers saying one cannot be saved unless he was circumcised, Acts 15:1,2. It was during this meeting that Peter rose up and said "
But we believe that we (Jews) shall be saved through the grace of the Lord Jesus, in like manner as they (Gentiles)." verse 11. Both Jews and Gentiles will be saved by God's grace in a "like manner" way. The Jews in Acts 2 had to repent (verse 38) it was an imperative the Jews had to obey to be saved, therefore the Gentiles must repent also to be saved in a "like manner" way.
Acts 20:21 "
Testifying both to the Jews, and also to the Greeks, repentance toward God, and faith toward our Lord Jesus Christ."
Acts 26:20 "
But shewed first unto them of Damascus, and at Jerusalem, and throughout all the coasts of Judaea, and then to the Gentiles, that they should repent and turn to God, and do works meet for repentance." (Note one has not turned to God until he first repents)
Paul taught to both Jews and Gentiles the necessity of repentance and Cornelius was not saved by God's grace in any different manner than the Jews or other Gentiles.