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Simplifying p2 + 12p + -2016 = 0 Reorder the terms: -2016 + 12p + p2 = 0 Solving -2016 + 12p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '2016' to each side of the equation. -2016 + 12p + 2016 + p2 = 0 + 2016 Reorder the terms: -2016 + 2016 + 12p + p2 = 0 + 2016 Combine like terms: -2016 + 2016 = 0 0 + 12p + p2 = 0 + 2016 12p + p2 = 0 + 2016 Combine like terms: 0 + 2016 = 2016 12p + p2 = 2016 The p term is 12p. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12p + 36 + p2 = 2016 + 36 Reorder the terms: 36 + 12p + p2 = 2016 + 36 Combine like terms: 2016 + 36 = 2052 36 + 12p + p2 = 2052 Factor a perfect square on the left side: (p + 6)(p + 6) = 2052 Calculate the square root of the right side: 45.299006612 Break this problem into two subproblems by setting (p + 6) equal to 45.299006612 and -45.299006612.Subproblem 1
p + 6 = 45.299006612 Simplifying p + 6 = 45.299006612 Reorder the terms: 6 + p = 45.299006612 Solving 6 + p = 45.299006612 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + p = 45.299006612 + -6 Combine like terms: 6 + -6 = 0 0 + p = 45.299006612 + -6 p = 45.299006612 + -6 Combine like terms: 45.299006612 + -6 = 39.299006612 p = 39.299006612 Simplifying p = 39.299006612Subproblem 2
p + 6 = -45.299006612 Simplifying p + 6 = -45.299006612 Reorder the terms: 6 + p = -45.299006612 Solving 6 + p = -45.299006612 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + p = -45.299006612 + -6 Combine like terms: 6 + -6 = 0 0 + p = -45.299006612 + -6 p = -45.299006612 + -6 Combine like terms: -45.299006612 + -6 = -51.299006612 p = -51.299006612 Simplifying p = -51.299006612Solution
The solution to the problem is based on the solutions from the subproblems. p = {39.299006612, -51.299006612}
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