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The operation will be completed inside the clinic within 30 minutes.
Literal
Operation [topic-は] clinic-inside [at-で] 30-minute within [in-に] is-completed.
A medical-service description. 以内 ('within X,' 'under X,' 'no more than X') is a formal quantity-capping suffix, attached to numbers or amounts to give a maximum. 三十分以内 = 'within 30 minutes,' 'in 30 minutes or less.' 完了する ('to complete, to be finished') is a slightly formal verb for completion of a task or process, more buttoned-up than 終わる. The frame ~に完了する uses に to mark the time frame within which completion occurs. Together the sentence reassures a patient about efficiency.