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Simplifying 2p2 + -24 = 16p Reorder the terms: -24 + 2p2 = 16p Solving -24 + 2p2 = 16p Solving for variable 'p'. Reorder the terms: -24 + -16p + 2p2 = 16p + -16p Combine like terms: 16p + -16p = 0 -24 + -16p + 2p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -8p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -8p + p2)' equal to zero and attempt to solve: Simplifying -12 + -8p + p2 = 0 Solving -12 + -8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -8p + 12 + p2 = 0 + 12 Reorder the terms: -12 + 12 + -8p + p2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -8p + p2 = 0 + 12 -8p + p2 = 0 + 12 Combine like terms: 0 + 12 = 12 -8p + p2 = 12 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 = 12 + 16 Reorder the terms: 16 + -8p + p2 = 12 + 16 Combine like terms: 12 + 16 = 28 16 + -8p + p2 = 28 Factor a perfect square on the left side: (p + -4)(p + -4) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (p + -4) equal to 5.291502622 and -5.291502622.Subproblem 1
p + -4 = 5.291502622 Simplifying p + -4 = 5.291502622 Reorder the terms: -4 + p = 5.291502622 Solving -4 + p = 5.291502622 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 = 5.291502622 + 4 Combine like terms: -4 + 4 = 0 0 + p = 5.291502622 + 4 p = 5.291502622 + 4 Combine like terms: 5.291502622 + 4 = 9.291502622 p = 9.291502622 Simplifying p = 9.291502622Subproblem 2
p + -4 = -5.291502622 Simplifying p + -4 = -5.291502622 Reorder the terms: -4 + p = -5.291502622 Solving -4 + p = -5.291502622 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 = -5.291502622 + 4 Combine like terms: -4 + 4 = 0 0 + p = -5.291502622 + 4 p = -5.291502622 + 4 Combine like terms: -5.291502622 + 4 = -1.291502622 p = -1.291502622 Simplifying p = -1.291502622Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.291502622, -1.291502622}Solution
p = {9.291502622, -1.291502622}
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