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Simplifying p2 + 2p + -54 = 6 Reorder the terms: -54 + 2p + p2 = 6 Solving -54 + 2p + p2 = 6 Solving for variable 'p'. Reorder the terms: -54 + -6 + 2p + p2 = 6 + -6 Combine like terms: -54 + -6 = -60 -60 + 2p + p2 = 6 + -6 Combine like terms: 6 + -6 = 0 -60 + 2p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 2p + 60 + p2 = 0 + 60 Reorder the terms: -60 + 60 + 2p + p2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 2p + p2 = 0 + 60 2p + p2 = 0 + 60 Combine like terms: 0 + 60 = 60 2p + p2 = 60 The p term is 2p. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2p + 1 + p2 = 60 + 1 Reorder the terms: 1 + 2p + p2 = 60 + 1 Combine like terms: 60 + 1 = 61 1 + 2p + p2 = 61 Factor a perfect square on the left side: (p + 1)(p + 1) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (p + 1) equal to 7.810249676 and -7.810249676.Subproblem 1
p + 1 = 7.810249676 Simplifying p + 1 = 7.810249676 Reorder the terms: 1 + p = 7.810249676 Solving 1 + p = 7.810249676 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = 7.810249676 + -1 Combine like terms: 1 + -1 = 0 0 + p = 7.810249676 + -1 p = 7.810249676 + -1 Combine like terms: 7.810249676 + -1 = 6.810249676 p = 6.810249676 Simplifying p = 6.810249676Subproblem 2
p + 1 = -7.810249676 Simplifying p + 1 = -7.810249676 Reorder the terms: 1 + p = -7.810249676 Solving 1 + p = -7.810249676 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = -7.810249676 + -1 Combine like terms: 1 + -1 = 0 0 + p = -7.810249676 + -1 p = -7.810249676 + -1 Combine like terms: -7.810249676 + -1 = -8.810249676 p = -8.810249676 Simplifying p = -8.810249676Solution
The solution to the problem is based on the solutions from the subproblems. p = {6.810249676, -8.810249676}
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