Maybe I can give some input.
Implement the following code by right-clicking the sheets tab and click on "View code". Paste the following in the big white field:
Private Sub Worksheet_Change(ByVal Target As Range)
If Intersect(Target, Columns("B:B")) Is Nothing Then Exit Sub
If Target.Value = "Completed" Then Target.Offset(0, 1).Value = Date
Whenever "Completed" is entered in column B, today's date is entered in the cell to the right.
If alterations are desired, let me know.