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Simplifying p2 + 8p + -81 = 10 Reorder the terms: -81 + 8p + p2 = 10 Solving -81 + 8p + p2 = 10 Solving for variable 'p'. Reorder the terms: -81 + -10 + 8p + p2 = 10 + -10 Combine like terms: -81 + -10 = -91 -91 + 8p + p2 = 10 + -10 Combine like terms: 10 + -10 = 0 -91 + 8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '91' to each side of the equation. -91 + 8p + 91 + p2 = 0 + 91 Reorder the terms: -91 + 91 + 8p + p2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + 8p + p2 = 0 + 91 8p + p2 = 0 + 91 Combine like terms: 0 + 91 = 91 8p + p2 = 91 The p term is 8p. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8p + 16 + p2 = 91 + 16 Reorder the terms: 16 + 8p + p2 = 91 + 16 Combine like terms: 91 + 16 = 107 16 + 8p + p2 = 107 Factor a perfect square on the left side: (p + 4)(p + 4) = 107 Calculate the square root of the right side: 10.344080433 Break this problem into two subproblems by setting (p + 4) equal to 10.344080433 and -10.344080433.Subproblem 1
p + 4 = 10.344080433 Simplifying p + 4 = 10.344080433 Reorder the terms: 4 + p = 10.344080433 Solving 4 + p = 10.344080433 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = 10.344080433 + -4 Combine like terms: 4 + -4 = 0 0 + p = 10.344080433 + -4 p = 10.344080433 + -4 Combine like terms: 10.344080433 + -4 = 6.344080433 p = 6.344080433 Simplifying p = 6.344080433Subproblem 2
p + 4 = -10.344080433 Simplifying p + 4 = -10.344080433 Reorder the terms: 4 + p = -10.344080433 Solving 4 + p = -10.344080433 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = -10.344080433 + -4 Combine like terms: 4 + -4 = 0 0 + p = -10.344080433 + -4 p = -10.344080433 + -4 Combine like terms: -10.344080433 + -4 = -14.344080433 p = -14.344080433 Simplifying p = -14.344080433Solution
The solution to the problem is based on the solutions from the subproblems. p = {6.344080433, -14.344080433}
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