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Simplifying 11p2 = 17 + 5p Solving 11p2 = 17 + 5p Solving for variable 'p'. Reorder the terms: -17 + -5p + 11p2 = 17 + 5p + -17 + -5p Reorder the terms: -17 + -5p + 11p2 = 17 + -17 + 5p + -5p Combine like terms: 17 + -17 = 0 -17 + -5p + 11p2 = 0 + 5p + -5p -17 + -5p + 11p2 = 5p + -5p Combine like terms: 5p + -5p = 0 -17 + -5p + 11p2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.545454545 + -0.4545454545p + p2 = 0 Move the constant term to the right: Add '1.545454545' to each side of the equation. -1.545454545 + -0.4545454545p + 1.545454545 + p2 = 0 + 1.545454545 Reorder the terms: -1.545454545 + 1.545454545 + -0.4545454545p + p2 = 0 + 1.545454545 Combine like terms: -1.545454545 + 1.545454545 = 0.000000000 0.000000000 + -0.4545454545p + p2 = 0 + 1.545454545 -0.4545454545p + p2 = 0 + 1.545454545 Combine like terms: 0 + 1.545454545 = 1.545454545 -0.4545454545p + p2 = 1.545454545 The p term is -0.4545454545p. Take half its coefficient (-0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. -0.4545454545p + 0.05165289257 + p2 = 1.545454545 + 0.05165289257 Reorder the terms: 0.05165289257 + -0.4545454545p + p2 = 1.545454545 + 0.05165289257 Combine like terms: 1.545454545 + 0.05165289257 = 1.59710743757 0.05165289257 + -0.4545454545p + p2 = 1.59710743757 Factor a perfect square on the left side: (p + -0.2272727273)(p + -0.2272727273) = 1.59710743757 Calculate the square root of the right side: 1.263767161 Break this problem into two subproblems by setting (p + -0.2272727273) equal to 1.263767161 and -1.263767161.Subproblem 1
p + -0.2272727273 = 1.263767161 Simplifying p + -0.2272727273 = 1.263767161 Reorder the terms: -0.2272727273 + p = 1.263767161 Solving -0.2272727273 + p = 1.263767161 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + p = 1.263767161 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + p = 1.263767161 + 0.2272727273 p = 1.263767161 + 0.2272727273 Combine like terms: 1.263767161 + 0.2272727273 = 1.4910398883 p = 1.4910398883 Simplifying p = 1.4910398883Subproblem 2
p + -0.2272727273 = -1.263767161 Simplifying p + -0.2272727273 = -1.263767161 Reorder the terms: -0.2272727273 + p = -1.263767161 Solving -0.2272727273 + p = -1.263767161 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + p = -1.263767161 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + p = -1.263767161 + 0.2272727273 p = -1.263767161 + 0.2272727273 Combine like terms: -1.263767161 + 0.2272727273 = -1.0364944337 p = -1.0364944337 Simplifying p = -1.0364944337Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.4910398883, -1.0364944337}
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