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Simplifying P2 + 2P = 0.87 Reorder the terms: 2P + P2 = 0.87 Solving 2P + P2 = 0.87 Solving for variable 'P'. Reorder the terms: -0.87 + 2P + P2 = 0.87 + -0.87 Combine like terms: 0.87 + -0.87 = 0.00 -0.87 + 2P + P2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.87' to each side of the equation. -0.87 + 2P + 0.87 + P2 = 0.00 + 0.87 Reorder the terms: -0.87 + 0.87 + 2P + P2 = 0.00 + 0.87 Combine like terms: -0.87 + 0.87 = 0.00 0.00 + 2P + P2 = 0.00 + 0.87 2P + P2 = 0.00 + 0.87 Combine like terms: 0.00 + 0.87 = 0.87 2P + P2 = 0.87 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 = 0.87 + 1 Reorder the terms: 1 + 2P + P2 = 0.87 + 1 Combine like terms: 0.87 + 1 = 1.87 1 + 2P + P2 = 1.87 Factor a perfect square on the left side: (P + 1)(P + 1) = 1.87 Calculate the square root of the right side: 1.367479433 Break this problem into two subproblems by setting (P + 1) equal to 1.367479433 and -1.367479433.Subproblem 1
P + 1 = 1.367479433 Simplifying P + 1 = 1.367479433 Reorder the terms: 1 + P = 1.367479433 Solving 1 + P = 1.367479433 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 = 1.367479433 + -1 Combine like terms: 1 + -1 = 0 0 + P = 1.367479433 + -1 P = 1.367479433 + -1 Combine like terms: 1.367479433 + -1 = 0.367479433 P = 0.367479433 Simplifying P = 0.367479433Subproblem 2
P + 1 = -1.367479433 Simplifying P + 1 = -1.367479433 Reorder the terms: 1 + P = -1.367479433 Solving 1 + P = -1.367479433 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 = -1.367479433 + -1 Combine like terms: 1 + -1 = 0 0 + P = -1.367479433 + -1 P = -1.367479433 + -1 Combine like terms: -1.367479433 + -1 = -2.367479433 P = -2.367479433 Simplifying P = -2.367479433Solution
The solution to the problem is based on the solutions from the subproblems. P = {0.367479433, -2.367479433}
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