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Simplifying 2p2 + -59p + 27 = 0 Reorder the terms: 27 + -59p + 2p2 = 0 Solving 27 + -59p + 2p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13.5 + -29.5p + p2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + -29.5p + -13.5 + p2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + -29.5p + p2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -29.5p + p2 = 0 + -13.5 -29.5p + p2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 -29.5p + p2 = -13.5 The p term is -29.5p. Take half its coefficient (-14.75). Square it (217.5625) and add it to both sides. Add '217.5625' to each side of the equation. -29.5p + 217.5625 + p2 = -13.5 + 217.5625 Reorder the terms: 217.5625 + -29.5p + p2 = -13.5 + 217.5625 Combine like terms: -13.5 + 217.5625 = 204.0625 217.5625 + -29.5p + p2 = 204.0625 Factor a perfect square on the left side: (p + -14.75)(p + -14.75) = 204.0625 Calculate the square root of the right side: 14.285044627 Break this problem into two subproblems by setting (p + -14.75) equal to 14.285044627 and -14.285044627.Subproblem 1
p + -14.75 = 14.285044627 Simplifying p + -14.75 = 14.285044627 Reorder the terms: -14.75 + p = 14.285044627 Solving -14.75 + p = 14.285044627 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + p = 14.285044627 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + p = 14.285044627 + 14.75 p = 14.285044627 + 14.75 Combine like terms: 14.285044627 + 14.75 = 29.035044627 p = 29.035044627 Simplifying p = 29.035044627Subproblem 2
p + -14.75 = -14.285044627 Simplifying p + -14.75 = -14.285044627 Reorder the terms: -14.75 + p = -14.285044627 Solving -14.75 + p = -14.285044627 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + p = -14.285044627 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + p = -14.285044627 + 14.75 p = -14.285044627 + 14.75 Combine like terms: -14.285044627 + 14.75 = 0.464955373 p = 0.464955373 Simplifying p = 0.464955373Solution
The solution to the problem is based on the solutions from the subproblems. p = {29.035044627, 0.464955373}
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