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Simplifying 5p + 28 = 88 + -1p * p Reorder the terms: 28 + 5p = 88 + -1p * p Multiply p * p 28 + 5p = 88 + -1p2 Solving 28 + 5p = 88 + -1p2 Solving for variable 'p'. Reorder the terms: 28 + -88 + 5p + p2 = 88 + -1p2 + -88 + p2 Combine like terms: 28 + -88 = -60 -60 + 5p + p2 = 88 + -1p2 + -88 + p2 Reorder the terms: -60 + 5p + p2 = 88 + -88 + -1p2 + p2 Combine like terms: 88 + -88 = 0 -60 + 5p + p2 = 0 + -1p2 + p2 -60 + 5p + p2 = -1p2 + p2 Combine like terms: -1p2 + p2 = 0 -60 + 5p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 5p + 60 + p2 = 0 + 60 Reorder the terms: -60 + 60 + 5p + p2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 5p + p2 = 0 + 60 5p + p2 = 0 + 60 Combine like terms: 0 + 60 = 60 5p + p2 = 60 The p term is 5p. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5p + 6.25 + p2 = 60 + 6.25 Reorder the terms: 6.25 + 5p + p2 = 60 + 6.25 Combine like terms: 60 + 6.25 = 66.25 6.25 + 5p + p2 = 66.25 Factor a perfect square on the left side: (p + 2.5)(p + 2.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (p + 2.5) equal to 8.139410298 and -8.139410298.Subproblem 1
p + 2.5 = 8.139410298 Simplifying p + 2.5 = 8.139410298 Reorder the terms: 2.5 + p = 8.139410298 Solving 2.5 + p = 8.139410298 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = 8.139410298 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = 8.139410298 + -2.5 p = 8.139410298 + -2.5 Combine like terms: 8.139410298 + -2.5 = 5.639410298 p = 5.639410298 Simplifying p = 5.639410298Subproblem 2
p + 2.5 = -8.139410298 Simplifying p + 2.5 = -8.139410298 Reorder the terms: 2.5 + p = -8.139410298 Solving 2.5 + p = -8.139410298 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = -8.139410298 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = -8.139410298 + -2.5 p = -8.139410298 + -2.5 Combine like terms: -8.139410298 + -2.5 = -10.639410298 p = -10.639410298 Simplifying p = -10.639410298Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.639410298, -10.639410298}
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