"She decided to eat."
Translation:Ela decidiu comer.
It's a rule of the language. It's called "regência verbal", and basically states that certain prepositions will follow certain verbs to give them a meaning (and that might change whether what follows is another verb or a noun). Just like in English you need to "listen to" something, but you can only "hear" something, in Portuguese we have this system.
An introductory book (in Portuguese, but of fairly easy reading) on this issue can be found as a link on our course newsletter for last month (Section "Notes from the Lusosphere - Portuguese Language"; you can also Ctrl+F and search for "regência verbal").
Is this a transitive and intransitive thing? It's possible to have a two-word sentence such as "she ate" and not to have a two-word sentence like "she began". So can we presume that if the verb is intransitive (in english, at least. I don't know how they match in Portuguese), it needs to have a preposition after?