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Simplifying 2p2 + -27p + 30 = 0 Reorder the terms: 30 + -27p + 2p2 = 0 Solving 30 + -27p + 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'. 15 + -13.5p + p2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -13.5p + -15 + p2 = 0 + -15 Reorder the terms: 15 + -15 + -13.5p + p2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -13.5p + p2 = 0 + -15 -13.5p + p2 = 0 + -15 Combine like terms: 0 + -15 = -15 -13.5p + p2 = -15 The p term is -13.5p. Take half its coefficient (-6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. -13.5p + 45.5625 + p2 = -15 + 45.5625 Reorder the terms: 45.5625 + -13.5p + p2 = -15 + 45.5625 Combine like terms: -15 + 45.5625 = 30.5625 45.5625 + -13.5p + p2 = 30.5625 Factor a perfect square on the left side: (p + -6.75)(p + -6.75) = 30.5625 Calculate the square root of the right side: 5.528336097 Break this problem into two subproblems by setting (p + -6.75) equal to 5.528336097 and -5.528336097.Subproblem 1
p + -6.75 = 5.528336097 Simplifying p + -6.75 = 5.528336097 Reorder the terms: -6.75 + p = 5.528336097 Solving -6.75 + p = 5.528336097 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + p = 5.528336097 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + p = 5.528336097 + 6.75 p = 5.528336097 + 6.75 Combine like terms: 5.528336097 + 6.75 = 12.278336097 p = 12.278336097 Simplifying p = 12.278336097Subproblem 2
p + -6.75 = -5.528336097 Simplifying p + -6.75 = -5.528336097 Reorder the terms: -6.75 + p = -5.528336097 Solving -6.75 + p = -5.528336097 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + p = -5.528336097 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + p = -5.528336097 + 6.75 p = -5.528336097 + 6.75 Combine like terms: -5.528336097 + 6.75 = 1.221663903 p = 1.221663903 Simplifying p = 1.221663903Solution
The solution to the problem is based on the solutions from the subproblems. p = {12.278336097, 1.221663903}
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