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Simplifying 2p2 + -55p + 23 = 0 Reorder the terms: 23 + -55p + 2p2 = 0 Solving 23 + -55p + 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'. 11.5 + -27.5p + p2 = 0 Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + -27.5p + -11.5 + p2 = 0 + -11.5 Reorder the terms: 11.5 + -11.5 + -27.5p + p2 = 0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + -27.5p + p2 = 0 + -11.5 -27.5p + p2 = 0 + -11.5 Combine like terms: 0 + -11.5 = -11.5 -27.5p + p2 = -11.5 The p term is -27.5p. Take half its coefficient (-13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. -27.5p + 189.0625 + p2 = -11.5 + 189.0625 Reorder the terms: 189.0625 + -27.5p + p2 = -11.5 + 189.0625 Combine like terms: -11.5 + 189.0625 = 177.5625 189.0625 + -27.5p + p2 = 177.5625 Factor a perfect square on the left side: (p + -13.75)(p + -13.75) = 177.5625 Calculate the square root of the right side: 13.325257971 Break this problem into two subproblems by setting (p + -13.75) equal to 13.325257971 and -13.325257971.Subproblem 1
p + -13.75 = 13.325257971 Simplifying p + -13.75 = 13.325257971 Reorder the terms: -13.75 + p = 13.325257971 Solving -13.75 + p = 13.325257971 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + p = 13.325257971 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + p = 13.325257971 + 13.75 p = 13.325257971 + 13.75 Combine like terms: 13.325257971 + 13.75 = 27.075257971 p = 27.075257971 Simplifying p = 27.075257971Subproblem 2
p + -13.75 = -13.325257971 Simplifying p + -13.75 = -13.325257971 Reorder the terms: -13.75 + p = -13.325257971 Solving -13.75 + p = -13.325257971 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + p = -13.325257971 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + p = -13.325257971 + 13.75 p = -13.325257971 + 13.75 Combine like terms: -13.325257971 + 13.75 = 0.424742029 p = 0.424742029 Simplifying p = 0.424742029Solution
The solution to the problem is based on the solutions from the subproblems. p = {27.075257971, 0.424742029}
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