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Simplifying P2 + -1P + 0.25 = 0 Reorder the terms: 0.25 + -1P + P2 = 0 Solving 0.25 + -1P + P2 = 0 Solving for variable 'P'. Begin completing the square. Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1P + -0.25 + P2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1P + P2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1P + P2 = 0 + -0.25 -1P + P2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1P + P2 = -0.25 The P term is -1P. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1P + 0.25 + P2 = -0.25 + 0.25 Reorder the terms: 0.25 + -1P + P2 = -0.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.25 + -1P + P2 = 0.00 Factor a perfect square on the left side: (P + -0.5)(P + -0.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (P + -0.5) equal to 0.00 and 0.00.Subproblem 1
P + -0.5 = 0.00 Simplifying P + -0.5 = 0.00 Reorder the terms: -0.5 + P = 0.00 Solving -0.5 + P = 0.00 Solving for variable 'P'. Move all terms containing P to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + P = 0.00 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + P = 0.00 + 0.5 P = 0.00 + 0.5 Combine like terms: 0.00 + 0.5 = 0.5 P = 0.5 Simplifying P = 0.5Subproblem 2
P + -0.5 = 0.00 Simplifying P + -0.5 = 0.00 Reorder the terms: -0.5 + P = 0.00 Solving -0.5 + P = 0.00 Solving for variable 'P'. Move all terms containing P to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + P = 0.00 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + P = 0.00 + 0.5 P = 0.00 + 0.5 Combine like terms: 0.00 + 0.5 = 0.5 P = 0.5 Simplifying P = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. P = {0.5, 0.5}
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