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Simplifying 2p2 + 32p = -22 Reorder the terms: 32p + 2p2 = -22 Solving 32p + 2p2 = -22 Solving for variable 'p'. Reorder the terms: 22 + 32p + 2p2 = -22 + 22 Combine like terms: -22 + 22 = 0 22 + 32p + 2p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(11 + 16p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + 16p + p2)' equal to zero and attempt to solve: Simplifying 11 + 16p + p2 = 0 Solving 11 + 16p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 16p + -11 + p2 = 0 + -11 Reorder the terms: 11 + -11 + 16p + p2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 16p + p2 = 0 + -11 16p + p2 = 0 + -11 Combine like terms: 0 + -11 = -11 16p + p2 = -11 The p term is 16p. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16p + 64 + p2 = -11 + 64 Reorder the terms: 64 + 16p + p2 = -11 + 64 Combine like terms: -11 + 64 = 53 64 + 16p + p2 = 53 Factor a perfect square on the left side: (p + 8)(p + 8) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (p + 8) equal to 7.280109889 and -7.280109889.Subproblem 1
p + 8 = 7.280109889 Simplifying p + 8 = 7.280109889 Reorder the terms: 8 + p = 7.280109889 Solving 8 + p = 7.280109889 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + p = 7.280109889 + -8 Combine like terms: 8 + -8 = 0 0 + p = 7.280109889 + -8 p = 7.280109889 + -8 Combine like terms: 7.280109889 + -8 = -0.719890111 p = -0.719890111 Simplifying p = -0.719890111Subproblem 2
p + 8 = -7.280109889 Simplifying p + 8 = -7.280109889 Reorder the terms: 8 + p = -7.280109889 Solving 8 + p = -7.280109889 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + p = -7.280109889 + -8 Combine like terms: 8 + -8 = 0 0 + p = -7.280109889 + -8 p = -7.280109889 + -8 Combine like terms: -7.280109889 + -8 = -15.280109889 p = -15.280109889 Simplifying p = -15.280109889Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.719890111, -15.280109889}Solution
p = {-0.719890111, -15.280109889}
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