How is this word "совершившимся" in the following sentence derived?

Question

How is the word "совершившимся" derived? The sentence is:

Меня поставили перед совершившимся фактом

I take it the root verb is совершить.

Answer 1

Let's make the morphological analysis of the word:

со-верш-и-вш-им-ся:

• со- is a prefix
• -верш- is the root.

The two above define the semantics of the word, meaning "to complete". This is Russian form of the prefix, though, as @shabunc noted, CS form с- (свершившимся) is more widely used in this context.

• -и- is a suffix defining perfective aspect
• -вш- is a suffix defining active participle
• -им- is a flective postfix (окончание) defining single number and instrumental case
• -ся is a particle (merged with the word) defining reflexivity.

Hence, we have a past perfective reflexive active participle in sg. inst. (действительное возвратное причастие совершенного вида прошедшего времени в творительном падеже единственного числа)

Answer 2

Actually the phrase is slightly outdated, the correct modern form is

меня поставили перед свершившимся фактом.

from свершиться - to happen (about something that have been expected to happen).

Though совершившимся is technically possible, it is used nowadays very rarely.