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Simplifying p2 + -8p + -96 = 0 Reorder the terms: -96 + -8p + p2 = 0 Solving -96 + -8p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + -8p + 96 + p2 = 0 + 96 Reorder the terms: -96 + 96 + -8p + p2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + -8p + p2 = 0 + 96 -8p + p2 = 0 + 96 Combine like terms: 0 + 96 = 96 -8p + p2 = 96 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 = 96 + 16 Reorder the terms: 16 + -8p + p2 = 96 + 16 Combine like terms: 96 + 16 = 112 16 + -8p + p2 = 112 Factor a perfect square on the left side: (p + -4)(p + -4) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (p + -4) equal to 10.583005244 and -10.583005244.Subproblem 1
p + -4 = 10.583005244 Simplifying p + -4 = 10.583005244 Reorder the terms: -4 + p = 10.583005244 Solving -4 + p = 10.583005244 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 = 10.583005244 + 4 Combine like terms: -4 + 4 = 0 0 + p = 10.583005244 + 4 p = 10.583005244 + 4 Combine like terms: 10.583005244 + 4 = 14.583005244 p = 14.583005244 Simplifying p = 14.583005244Subproblem 2
p + -4 = -10.583005244 Simplifying p + -4 = -10.583005244 Reorder the terms: -4 + p = -10.583005244 Solving -4 + p = -10.583005244 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 = -10.583005244 + 4 Combine like terms: -4 + 4 = 0 0 + p = -10.583005244 + 4 p = -10.583005244 + 4 Combine like terms: -10.583005244 + 4 = -6.583005244 p = -6.583005244 Simplifying p = -6.583005244Solution
The solution to the problem is based on the solutions from the subproblems. p = {14.583005244, -6.583005244}
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