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Simplifying p2 + 2p + -44 = 0 Reorder the terms: -44 + 2p + p2 = 0 Solving -44 + 2p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 2p + 44 + p2 = 0 + 44 Reorder the terms: -44 + 44 + 2p + p2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 2p + p2 = 0 + 44 2p + p2 = 0 + 44 Combine like terms: 0 + 44 = 44 2p + p2 = 44 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 = 44 + 1 Reorder the terms: 1 + 2p + p2 = 44 + 1 Combine like terms: 44 + 1 = 45 1 + 2p + p2 = 45 Factor a perfect square on the left side: (p + 1)(p + 1) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (p + 1) equal to 6.708203933 and -6.708203933.Subproblem 1
p + 1 = 6.708203933 Simplifying p + 1 = 6.708203933 Reorder the terms: 1 + p = 6.708203933 Solving 1 + p = 6.708203933 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 = 6.708203933 + -1 Combine like terms: 1 + -1 = 0 0 + p = 6.708203933 + -1 p = 6.708203933 + -1 Combine like terms: 6.708203933 + -1 = 5.708203933 p = 5.708203933 Simplifying p = 5.708203933Subproblem 2
p + 1 = -6.708203933 Simplifying p + 1 = -6.708203933 Reorder the terms: 1 + p = -6.708203933 Solving 1 + p = -6.708203933 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 = -6.708203933 + -1 Combine like terms: 1 + -1 = 0 0 + p = -6.708203933 + -1 p = -6.708203933 + -1 Combine like terms: -6.708203933 + -1 = -7.708203933 p = -7.708203933 Simplifying p = -7.708203933Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.708203933, -7.708203933}
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