A poll indicates that x months after a particular candidate for public office declares her candidacy, she will have the support of S(x) percent of the voters, where

If the election is held in November, when should the politician announce her candidacy? Should she expect to win if she needs at least 50% of the vote?

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S(x) -(-x²³ + 6x² + 63x + 1,080) 29 for 0≤x≤ 12