Page "The Return of the Archons" Paragraph 6

Kirk and Spock manage to convince the machine that running the planet as it has been is wrong and the people are being kept as uncreative slaves.

They manage to convince the machine that it has violated its own prime directive.

The machine realizes its mistake and self-destructs, thus freeing the people of Beta III.

Kirk agrees to leave Federation advisors and educators on the planet to help the civilization advance, free of Landru's dominance.