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Simplifying p2 + 2p + 16 = 63 Reorder the terms: 16 + 2p + p2 = 63 Solving 16 + 2p + p2 = 63 Solving for variable 'p'. Reorder the terms: 16 + -63 + 2p + p2 = 63 + -63 Combine like terms: 16 + -63 = -47 -47 + 2p + p2 = 63 + -63 Combine like terms: 63 + -63 = 0 -47 + 2p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 2p + 47 + p2 = 0 + 47 Reorder the terms: -47 + 47 + 2p + p2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 2p + p2 = 0 + 47 2p + p2 = 0 + 47 Combine like terms: 0 + 47 = 47 2p + p2 = 47 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 = 47 + 1 Reorder the terms: 1 + 2p + p2 = 47 + 1 Combine like terms: 47 + 1 = 48 1 + 2p + p2 = 48 Factor a perfect square on the left side: (p + 1)(p + 1) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (p + 1) equal to 6.92820323 and -6.92820323.Subproblem 1
p + 1 = 6.92820323 Simplifying p + 1 = 6.92820323 Reorder the terms: 1 + p = 6.92820323 Solving 1 + p = 6.92820323 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 = 6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + p = 6.92820323 + -1 p = 6.92820323 + -1 Combine like terms: 6.92820323 + -1 = 5.92820323 p = 5.92820323 Simplifying p = 5.92820323Subproblem 2
p + 1 = -6.92820323 Simplifying p + 1 = -6.92820323 Reorder the terms: 1 + p = -6.92820323 Solving 1 + p = -6.92820323 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 = -6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + p = -6.92820323 + -1 p = -6.92820323 + -1 Combine like terms: -6.92820323 + -1 = -7.92820323 p = -7.92820323 Simplifying p = -7.92820323Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.92820323, -7.92820323}
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