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Simplifying (P2) + -2P = 5 P2 + -2P = 5 Reorder the terms: -2P + P2 = 5 Solving -2P + P2 = 5 Solving for variable 'P'. Reorder the terms: -5 + -2P + P2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -2P + P2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -2P + 5 + P2 = 0 + 5 Reorder the terms: -5 + 5 + -2P + P2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2P + P2 = 0 + 5 -2P + P2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2P + P2 = 5 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 = 5 + 1 Reorder the terms: 1 + -2P + P2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + -2P + P2 = 6 Factor a perfect square on the left side: (P + -1)(P + -1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (P + -1) equal to 2.449489743 and -2.449489743.Subproblem 1
P + -1 = 2.449489743 Simplifying P + -1 = 2.449489743 Reorder the terms: -1 + P = 2.449489743 Solving -1 + P = 2.449489743 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 = 2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + P = 2.449489743 + 1 P = 2.449489743 + 1 Combine like terms: 2.449489743 + 1 = 3.449489743 P = 3.449489743 Simplifying P = 3.449489743Subproblem 2
P + -1 = -2.449489743 Simplifying P + -1 = -2.449489743 Reorder the terms: -1 + P = -2.449489743 Solving -1 + P = -2.449489743 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 = -2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + P = -2.449489743 + 1 P = -2.449489743 + 1 Combine like terms: -2.449489743 + 1 = -1.449489743 P = -1.449489743 Simplifying P = -1.449489743Solution
The solution to the problem is based on the solutions from the subproblems. P = {3.449489743, -1.449489743}
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