This is the 492nd most frequent Russian word.
решили
"Decided."
Here, 'решили' indicates the decision-making action of the third person plural.
Они решили поехать на море.
They decided to go to the sea.
In this sentence, 'решил' refers to solving something, indicating accomplishment or completion.
Ты решил задачу очень быстро.
You solved the problem very quickly.
Here, 'решили' again relates to making a decision, but has the connotation of planning or agreeing to take an action.