Они решили расстаться.

A word-by-word breakdown:

• Они = they
• решили = decided
• расстаться = to part / to separate / to break up

So the structure is literally They decided to separate.

Yes, решить can mean both to decide and to solve.

The meaning depends on what comes after it:

• решить + infinitive = to decide to do something
  
  • решили расстаться = they decided to break up
• решить + noun = to solve something
  • решить задачу = to solve a problem
  • решить вопрос = to settle/resolve a question

So here, because решили is followed by the infinitive расстаться, it clearly means decided.

Because it is past tense plural.

In Russian past tense, the verb agrees with the subject in number and, in the singular, also gender:

• он решил = he decided
• она решила = she decided
• оно решило = it decided
• они решили = they decided

Since the subject is они (they), the verb must be plural: решили.

Because Russian does not use a separate word like English to before the infinitive.

The infinitive form itself already carries that meaning. So:

• решили расстаться = decided to break up

Here расстаться is the infinitive form, so no extra word is needed.

The ending -ся often makes a verb reflexive, but in many verbs it has broader meanings than simple English reflexives like wash oneself.

In расстаться, it helps form a verb meaning to separate / part from each other. It is not really best translated word-for-word as separate themselves in normal English, but that idea is part of the grammar.

So:

• расстать is not the normal verb you would use here
• расстаться is the actual dictionary form meaning to part / break up

In this sentence, -ся is just part of the standard verb form you need.

This is a question of aspect.

• расстаться = perfective
• расставаться = imperfective

Very roughly:

• perfective focuses on the action as a whole, as a completed event
• imperfective focuses on process, repetition, or ongoing action

Here, расстаться fits because the idea is to make the decision to break up / to separate as a single event.

Examples:

• Они решили расстаться. = They decided to break up.
• Они долго расставались. = They were separating for a long time / breaking up was a long process.
• Им было трудно расставаться. = It was hard for them to part.

Again, this is aspect:

• решить → решили = perfective, decided
• решать → решали = imperfective, were deciding / used to decide

In this sentence, the speaker is talking about a completed decision: they decided. That is why решили is natural.

If you said Они решали расстаться, it would sound like They were deciding whether to break up, which is a different meaning and is less natural without more context.

No. It can mean several related things depending on context:

• to part
• to separate
• to say goodbye
• to break up (in a romantic sense)
• sometimes to part with something

In Они решили расстаться, many learners will understand it as They decided to break up, especially if the context is about a couple. But without context, it can also mean They decided to part ways more generally.

Yes, but only if the context makes it clear who is being talked about.

Russian often drops subjects when they are understood. So you might hear:

• Решили расстаться.

However, there is an important difference from present tense verbs: in the past tense plural, the verb form does not show person. So решили by itself could mean:

• they decided
• we decided
• you (plural/formal) decided

So omitting они is possible, but it relies heavily on context.

No, Russian word order is fairly flexible, although Они решили расстаться is the most neutral order.

Other orders are possible, but they change emphasis:

• Они решили расстаться. = neutral
• Решили они расстаться. = more marked; can sound narrative or contrastive
• Расстаться они решили. = emphasizes breaking up specifically

So the original sentence is the most natural basic version for a learner to remember.

It is pronounced roughly as:

• расста́ться
• approximately ras-STAT-sa

A few useful notes:

• the stress is on -та́-
• the ending -ться is usually pronounced like -ца
• the double сс comes from the structure of the word: the prefix рас- joins a part beginning with с, so both с letters appear in spelling

The whole sentence is stressed like this:

• Они́ реши́ли расста́ться.

It is neutral standard Russian.

It works well in everyday speech, writing, books, and conversation. It is not especially slangy, poetic, or formal.

Depending on context, more colloquial alternatives might be used, especially for romantic relationships, but Они решили расстаться is a very normal and natural sentence.