It has occurred to me after reading over this thread that you may be trying to write a date field value to a date/time field value.
Now() is a function that gives you the current date 'and' time of day. Are both [Completion Date] and [Scheduled Date] Date/Time fields? Or, is one of them just a Date field?
Are you certain the two dates will always match? Is it not possible that [Completion Date] may occur sooner than or later than [Scheduled Date] ?
You would auto populate the [Completion Date] field much like Matthew said, except when [Status] = "Complete", change [Completion Date] to the current date in the form rule. You will still be able to edit the [Completion Date] field manually, the form rule allows you to populate the date field automatically upon a certain condition.
In the form rule, you may want to check the box that says, "change occurs when condition changes from false to true". This will keep the [Complete Date] from changing to the current date every time the record is edited subsequent to its completion.