32 Then they preached the word of the Lord to him and to all his household.<quoted text>
Ac 16:30 And brought them out, and said, Sirs, what must I do to be saved?
Lu 3:10; Ac 2:37; 9:6
31 And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.
Joh 3:16,36; 6:47; 1Jo 5:10
I see nothing about the requirement of being baptized to be saved in the parallel verses listed for Ac 16:30-31
33 Late as it was, he took them to wash their wounds, and was baptised then and there with all his household.