2 answers
In case, If you had to write a trigger, it would be something like following mockup: trigger task_After on Task (after insert)
{
List<Account> AccountsToUpdate = new List<Account>();
for (Task t: Trigger.new)
{
if (t.Status=='Completed')
{
Account a = new Account(Id=t.WhatId);
a.Account_completion_Status = t.Status;
AccountsToUpdate.add(a);
}
}
try {
update AccountsToUpdate;
} catch (system.Dmlexception e) {
system.debug (e);
}
}