Dogovorili smo se za petak.

It is the 1st person plural perfect tense of dogovoriti se, so it means we agreed, we arranged, or we came to an agreement.

A very literal breakdown is:

• dogovorili = agreed / arranged
• smo = we have / we did (the auxiliary to be used to form the perfect)
• se = a reflexive particle that belongs to this verb

So dogovorili smo se is best learned as a whole verbal expression: we agreed / we arranged.

Yes. The verb here is dogovoriti se, not just dogovoriti.

In Serbian, many verbs are used with se, and the meaning is not always literally reflexive in the English sense. Here, dogovoriti se means to come to an agreement / to arrange something together.

So:

• dogovoriti se = to agree, to make an arrangement
• dogovoriti without se usually has a different meaning, more like to arrange/fix something or to settle something

For learners, it is safest to memorize this as a fixed verb:

• dogovoriti se = to agree / arrange

Because Serbian usually does not need an explicit subject pronoun when the verb already shows the person and number.

Here, smo plus dogovorili clearly tells you the subject is we.

So Serbian often says:

• Dogovorili smo se = We agreed

If you say Mi smo se dogovorili, the mi is added only for emphasis, contrast, or clarity:

• Mi smo se dogovorili, a oni nisu. = We agreed, but they didn’t.

This is the perfect tense in Serbian.

It is formed with:

• the past active participle: dogovorili
• the auxiliary biti in the present tense: smo

So:

• dogovorili smo se = we agreed / we have agreed

In everyday Serbian, the perfect tense is the normal way to talk about completed past actions.

Because the participle has to agree with the subject.

The subject is we, and in a mixed or unspecified group, Serbian normally uses the masculine plural form:

• dogovorili

Compare:

• dogovorili smo se = we agreed (mixed group or at least one male, or unspecified)
• dogovorile smo se = we agreed (all-female group)

So if a group of women is speaking, they would usually say:

• Dogovorile smo se za petak.

Because za + accusative is commonly used for something planned, scheduled, reserved, or intended for a certain time.

So:

• za petak = for Friday

This gives the idea that the arrangement is set for that day.

Similar examples:

• Zakazali smo sastanak za petak. = We scheduled the meeting for Friday.
• Ostavili smo to za sutra. = We left that for tomorrow.

Petak is in the accusative singular because it follows za in this meaning.

However, petak is a masculine inanimate noun, and for many masculine inanimate nouns, the accusative singular looks the same as the nominative singular.

So:

• nominative: petak
• accusative: petak

That is why you do not see a visible change here, even though the case has changed.

In this sentence, the most natural idea is for Friday: something was arranged to take place on Friday.

In English, depending on context, you might translate it as:

• We arranged it for Friday
• We agreed on Friday
• We agreed for Friday

But the Serbian phrasing most strongly suggests a scheduled time, not simply the day when the agreement happened.

So the sentence usually means:

• We arranged it for Friday.

If you wanted to stress that the agreement itself happened on Friday, you would more naturally use something like:

• Dogovorili smo se u petak. = We agreed on Friday.

This is a very common learner question.

• u petak = on Friday
  This usually tells you when something happens
• za petak = for Friday
  This usually tells you something is planned/scheduled for Friday

Compare:

• Sastanak je u petak. = The meeting is on Friday.

• Dogovorili smo sastanak za petak. = We arranged the meeting for Friday.

So in your sentence, za petak points to the day the arrangement is set for, not necessarily the day the agreement was made.

The infinitive is dogovoriti se.

This is a perfective verb, which means it presents the action as completed or as a single achieved result.

Its imperfective partner is:

• dogovarati se = to be agreeing / to be arranging / to negotiate

Compare:

• Dogovarali smo se ceo dan. = We were discussing/arranging it all day.
  (process, ongoing action)

• Dogovorili smo se. = We reached an agreement.
  (completed result)

Not if you want the same meaning.

Dogovorili smo se za petak is the natural way to say we agreed / arranged it for Friday.

If you remove se, the meaning changes or the sentence becomes unnatural/incomplete in this context.

So for this idea, keep the full reflexive verb:

• dogovoriti se

That is the form you should associate with to agree / to come to an arrangement.

No, Serbian word order is fairly flexible, although some orders sound more neutral than others.

The neutral version is:

• Dogovorili smo se za petak.

But you can also hear:

• Za petak smo se dogovorili.
• Dogovorili smo se za petak već juče.

Changing the word order usually changes emphasis, not the core meaning.

For example:

• Za petak smo se dogovorili puts more focus on Friday.

This happens because smo and se are both clitics in Serbian, and clitics tend to go in a special position in the sentence, usually near the beginning.

In standard word order, the perfect participle often comes first, followed by the auxiliary and then other clitics:

• Dogovorili smo se

This clitic placement is something learners gradually get used to. It is not random, but it does not work exactly like English word order.

A useful thing to remember is that this pattern is very common:

• Video sam ga. = I saw him.
• Dogovorili smo se. = We agreed.

Usually, yes.

Because dogovoriti se normally means that an agreement or arrangement was reached, it strongly suggests that the participants came to a shared decision.

So it is more mutual than simply:

• odlučili smo = we decided

With dogovorili smo se, the idea is:

• an agreement was made
• the details were settled
• there is now a plan

That is why it is a very natural phrase for arranging meetings, plans, dates, and appointments.