
festgelegt
fixed
Bindingly determined, defined, or decided. Describes something that can no longer be changed, or only with difficulty.
Der Termin für die Prüfung ist bereits festgelegt.
The date for the exam has already been fixed.
fixed / determined
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fixed
Bindingly determined, defined, or decided. Describes something that can no longer be changed, or only with difficulty.
Der Termin für die Prüfung ist bereits festgelegt.
The date for the exam has already been fixed.

to have decided
To have decided on and committed to a particular option, opinion, or course of action.
Ich habe mich noch nicht festgelegt, welches Auto ich kaufe.
I haven't decided yet which car I'm buying.
'Festgelegt' (fixed/determined) is the past participle of the separable verb 'festlegen' (to determine/fix). It consists of 'fest' (fixed/firm) and 'legen' (to lay) and literally means to lay something down so that it is fixed and no longer moves.
Wir müssen die Regeln für das Projekt genau festlegen.
We have to define the rules for the project precisely.
Since 'festlegen' (to determine/fix) is a separable verb, the prefix 'fest-' comes at the end in a main clause. However, the participle 'festgelegt' (fixed/determined) is always written as one word.
Die Firma legt die neuen Preise fest.
The company fixes the new prices.
Typical things that are 'festgelegt' (fixed/determined) are appointments, deadlines, rules, prices, goals, or an exact date.
Die Route für den Marathon ist jetzt endgültig festgelegt.
The route for the marathon is now finally fixed.
The expression 'sich festgelegt haben' (to have decided/committed oneself) means that a person has made a personal decision. It is always formed with a reflexive pronoun (mich, dich, sich, etc.).
Er hat sich schon für ein Studienfach festgelegt.
He has already decided on a field of study.
When you want to say what you have decided on, you use the preposition 'auf' followed by the accusative.
Sie hat sich auf ein Thema für ihre Masterarbeit festgelegt.
She has decided on a topic for her master's thesis.
certain / specific
When referring to an appointment or value, bestimmt identifies something specific and distinguishes it from other possibilities. Festgelegt additionally means that it has been decided on definitively and cannot be changed, or can only be changed with difficulty. Bestimmt fits a mere specification; festgelegt fits a binding decision.

Unser Termin am 15. Mai ist bereits verbindlich festgelegt.
Our appointment on May 15 has already been definitively fixed.
Wir treffen uns an einem bestimmten Termin im Mai.
We are meeting on a specific date in May.