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She painstakingly examined the company's performance.
Literal
She [topic-は] company [of-の] business-results [object-を] painstakingly examined.
丹念に is the adverb form of the na-adjective 丹念 ('careful, painstaking, meticulous'), describing the manner of doing something with close attention to detail. 業績 in a business context means a company's performance — earnings, results, track record — so the sentence pictures her going through the books or reports with a fine-tooth comb. The combination 丹念に調べる is a set-phrase-like collocation for thorough investigation; you'll see it in news writing about journalism, due diligence, audits.