Finding the distinct IDs from filtered data

this did not work for you ?

CALCULATE (
distinctcount(Training[trainee id]),
FILTER (
Training,
SEARCH ( "Completed", Training[Status],, 0 ) > 0
|| SEARCH ( "Complete", Training[Status],, 0) > 0
)
)

Anonymous  not sure i quite understand what you asking, did you say you tried this

Measure Trainees Completed Course =
CALCULATE (
    DISTINCTCOUNT ( [trainingid] ),
    FILTER (
        Training,
        SEARCH ( "Completed", Training[Status],, BLANK () ) > 0
            || SEARCH ( "Complete", Training[Status],, BLANK () ) > 0
    )
) but it didn't work? What are you trying to do?