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Simplifying p2 + -4p + -108 = 0 Reorder the terms: -108 + -4p + p2 = 0 Solving -108 + -4p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + -4p + 108 + p2 = 0 + 108 Reorder the terms: -108 + 108 + -4p + p2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + -4p + p2 = 0 + 108 -4p + p2 = 0 + 108 Combine like terms: 0 + 108 = 108 -4p + p2 = 108 The p term is -4p. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4p + 4 + p2 = 108 + 4 Reorder the terms: 4 + -4p + p2 = 108 + 4 Combine like terms: 108 + 4 = 112 4 + -4p + p2 = 112 Factor a perfect square on the left side: (p + -2)(p + -2) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (p + -2) equal to 10.583005244 and -10.583005244.Subproblem 1
p + -2 = 10.583005244 Simplifying p + -2 = 10.583005244 Reorder the terms: -2 + p = 10.583005244 Solving -2 + p = 10.583005244 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = 10.583005244 + 2 Combine like terms: -2 + 2 = 0 0 + p = 10.583005244 + 2 p = 10.583005244 + 2 Combine like terms: 10.583005244 + 2 = 12.583005244 p = 12.583005244 Simplifying p = 12.583005244Subproblem 2
p + -2 = -10.583005244 Simplifying p + -2 = -10.583005244 Reorder the terms: -2 + p = -10.583005244 Solving -2 + p = -10.583005244 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = -10.583005244 + 2 Combine like terms: -2 + 2 = 0 0 + p = -10.583005244 + 2 p = -10.583005244 + 2 Combine like terms: -10.583005244 + 2 = -8.583005244 p = -8.583005244 Simplifying p = -8.583005244Solution
The solution to the problem is based on the solutions from the subproblems. p = {12.583005244, -8.583005244}
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