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Simplifying -2p2 = 16p + 28 Reorder the terms: -2p2 = 28 + 16p Solving -2p2 = 28 + 16p Solving for variable 'p'. Reorder the terms: -28 + -16p + -2p2 = 28 + 16p + -28 + -16p Reorder the terms: -28 + -16p + -2p2 = 28 + -28 + 16p + -16p Combine like terms: 28 + -28 = 0 -28 + -16p + -2p2 = 0 + 16p + -16p -28 + -16p + -2p2 = 16p + -16p Combine like terms: 16p + -16p = 0 -28 + -16p + -2p2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(14 + 8p + p2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(14 + 8p + p2)' equal to zero and attempt to solve: Simplifying 14 + 8p + p2 = 0 Solving 14 + 8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 8p + -14 + p2 = 0 + -14 Reorder the terms: 14 + -14 + 8p + p2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 8p + p2 = 0 + -14 8p + p2 = 0 + -14 Combine like terms: 0 + -14 = -14 8p + p2 = -14 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 = -14 + 16 Reorder the terms: 16 + 8p + p2 = -14 + 16 Combine like terms: -14 + 16 = 2 16 + 8p + p2 = 2 Factor a perfect square on the left side: (p + 4)(p + 4) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (p + 4) equal to 1.414213562 and -1.414213562.Subproblem 1
p + 4 = 1.414213562 Simplifying p + 4 = 1.414213562 Reorder the terms: 4 + p = 1.414213562 Solving 4 + p = 1.414213562 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 = 1.414213562 + -4 Combine like terms: 4 + -4 = 0 0 + p = 1.414213562 + -4 p = 1.414213562 + -4 Combine like terms: 1.414213562 + -4 = -2.585786438 p = -2.585786438 Simplifying p = -2.585786438Subproblem 2
p + 4 = -1.414213562 Simplifying p + 4 = -1.414213562 Reorder the terms: 4 + p = -1.414213562 Solving 4 + p = -1.414213562 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 = -1.414213562 + -4 Combine like terms: 4 + -4 = 0 0 + p = -1.414213562 + -4 p = -1.414213562 + -4 Combine like terms: -1.414213562 + -4 = -5.414213562 p = -5.414213562 Simplifying p = -5.414213562Solution
The solution to the problem is based on the solutions from the subproblems. p = {-2.585786438, -5.414213562}Solution
p = {-2.585786438, -5.414213562}
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