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Simplifying P2 + P + -5 = 0 Reorder the terms: -5 + P + P2 = 0 Solving -5 + P + P2 = 0 Solving for variable 'P'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + P + 5 + P2 = 0 + 5 Reorder the terms: -5 + 5 + P + P2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + P + P2 = 0 + 5 P + P2 = 0 + 5 Combine like terms: 0 + 5 = 5 P + P2 = 5 The P term is P. 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. P + 0.25 + P2 = 5 + 0.25 Reorder the terms: 0.25 + P + P2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + P + P2 = 5.25 Factor a perfect square on the left side: (P + 0.5)(P + 0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (P + 0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
P + 0.5 = 2.291287847 Simplifying P + 0.5 = 2.291287847 Reorder the terms: 0.5 + P = 2.291287847 Solving 0.5 + P = 2.291287847 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 = 2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + P = 2.291287847 + -0.5 P = 2.291287847 + -0.5 Combine like terms: 2.291287847 + -0.5 = 1.791287847 P = 1.791287847 Simplifying P = 1.791287847Subproblem 2
P + 0.5 = -2.291287847 Simplifying P + 0.5 = -2.291287847 Reorder the terms: 0.5 + P = -2.291287847 Solving 0.5 + P = -2.291287847 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 = -2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + P = -2.291287847 + -0.5 P = -2.291287847 + -0.5 Combine like terms: -2.291287847 + -0.5 = -2.791287847 P = -2.791287847 Simplifying P = -2.791287847Solution
The solution to the problem is based on the solutions from the subproblems. P = {1.791287847, -2.791287847}
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