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How do I make a formula date field called "Completion Date" that captures the date when a multiple choice field called "Status" is set to a particular value like "Complete"?
The best way to do this is to flip the problem around on its head.
1) Instead of making the date field a formula field, make it a plain date field.
2) Then remove the choice of "Complete" from your multiple choice "Status" field.
3) Create a formula text field called "Computed Status".
4) Put the following formula into the formula property of the "Computed Status" field.
if(isnull([Completion Date]), [Status], "Complete")
5) Now in all your views and display record forms replace the "Status" field with the "Computed Status" field.
6) On custom forms you can use alternate label text to relabel the "Computed Status" field back to "Status".
Your users will now mark a record as "Complete" by simply entering a date in the "Completion Date" field. A blank date in the "Completion Date" field means the record's status is not complete.