Satisfied means content that what you wanted has been met. Nothing more is needed.
It takes with for the thing and that for a fact: satisfied with the result, satisfied that the work was done properly. That second pattern is formal and legal, since a court can be satisfied that something is true. There is a subtle limit to the word, since being satisfied is contentment rather than delight, and a satisfied customer is pleased rather than thrilled. Self-satisfied is a criticism and means smug.
1adjectivesatisfiedContent because your needs or expectations have been met.
“He seemed satisfied with the explanation.”
2adjectiveconvincedConvinced that something is true.
“The inspector was satisfied that nothing was wrong.”
Too few real examples of this word to estimate which sense is commonest.
Middle English
satisfyed
English, today
satisfied
From Middle English satisfyed, from satisfien. From Middle English satisfyed, i-satisfyed, i-satisfied, past participle of Middle English satisfien, equivalent to satisfy + -ed.
Etymology from Wiktionary, CC BY-SA