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Simplifying p(p + -0.105) = 5907 Reorder the terms: p(-0.105 + p) = 5907 (-0.105 * p + p * p) = 5907 (-0.105p + p2) = 5907 Solving -0.105p + p2 = 5907 Solving for variable 'p'. Reorder the terms: -5907 + -0.105p + p2 = 5907 + -5907 Combine like terms: 5907 + -5907 = 0 -5907 + -0.105p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '5907' to each side of the equation. -5907 + -0.105p + 5907 + p2 = 0 + 5907 Reorder the terms: -5907 + 5907 + -0.105p + p2 = 0 + 5907 Combine like terms: -5907 + 5907 = 0 0 + -0.105p + p2 = 0 + 5907 -0.105p + p2 = 0 + 5907 Combine like terms: 0 + 5907 = 5907 -0.105p + p2 = 5907 The p term is -0.105p. Take half its coefficient (-0.0525). Square it (0.00275625) and add it to both sides. Add '0.00275625' to each side of the equation. -0.105p + 0.00275625 + p2 = 5907 + 0.00275625 Reorder the terms: 0.00275625 + -0.105p + p2 = 5907 + 0.00275625 Combine like terms: 5907 + 0.00275625 = 5907.00275625 0.00275625 + -0.105p + p2 = 5907.00275625 Factor a perfect square on the left side: (p + -0.0525)(p + -0.0525) = 5907.00275625 Calculate the square root of the right side: 76.857028021 Break this problem into two subproblems by setting (p + -0.0525) equal to 76.857028021 and -76.857028021.Subproblem 1
p + -0.0525 = 76.857028021 Simplifying p + -0.0525 = 76.857028021 Reorder the terms: -0.0525 + p = 76.857028021 Solving -0.0525 + p = 76.857028021 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.0525' to each side of the equation. -0.0525 + 0.0525 + p = 76.857028021 + 0.0525 Combine like terms: -0.0525 + 0.0525 = 0.0000 0.0000 + p = 76.857028021 + 0.0525 p = 76.857028021 + 0.0525 Combine like terms: 76.857028021 + 0.0525 = 76.909528021 p = 76.909528021 Simplifying p = 76.909528021Subproblem 2
p + -0.0525 = -76.857028021 Simplifying p + -0.0525 = -76.857028021 Reorder the terms: -0.0525 + p = -76.857028021 Solving -0.0525 + p = -76.857028021 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.0525' to each side of the equation. -0.0525 + 0.0525 + p = -76.857028021 + 0.0525 Combine like terms: -0.0525 + 0.0525 = 0.0000 0.0000 + p = -76.857028021 + 0.0525 p = -76.857028021 + 0.0525 Combine like terms: -76.857028021 + 0.0525 = -76.804528021 p = -76.804528021 Simplifying p = -76.804528021Solution
The solution to the problem is based on the solutions from the subproblems. p = {76.909528021, -76.804528021}
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