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Simplifying 25P + P2 = 2500 Solving 25P + P2 = 2500 Solving for variable 'P'. Reorder the terms: -2500 + 25P + P2 = 2500 + -2500 Combine like terms: 2500 + -2500 = 0 -2500 + 25P + P2 = 0 Begin completing the square. Move the constant term to the right: Add '2500' to each side of the equation. -2500 + 25P + 2500 + P2 = 0 + 2500 Reorder the terms: -2500 + 2500 + 25P + P2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + 25P + P2 = 0 + 2500 25P + P2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 25P + P2 = 2500 The P term is 25P. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25P + 156.25 + P2 = 2500 + 156.25 Reorder the terms: 156.25 + 25P + P2 = 2500 + 156.25 Combine like terms: 2500 + 156.25 = 2656.25 156.25 + 25P + P2 = 2656.25 Factor a perfect square on the left side: (P + 12.5)(P + 12.5) = 2656.25 Calculate the square root of the right side: 51.53882032 Break this problem into two subproblems by setting (P + 12.5) equal to 51.53882032 and -51.53882032.Subproblem 1
P + 12.5 = 51.53882032 Simplifying P + 12.5 = 51.53882032 Reorder the terms: 12.5 + P = 51.53882032 Solving 12.5 + P = 51.53882032 Solving for variable 'P'. Move all terms containing P to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + P = 51.53882032 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + P = 51.53882032 + -12.5 P = 51.53882032 + -12.5 Combine like terms: 51.53882032 + -12.5 = 39.03882032 P = 39.03882032 Simplifying P = 39.03882032Subproblem 2
P + 12.5 = -51.53882032 Simplifying P + 12.5 = -51.53882032 Reorder the terms: 12.5 + P = -51.53882032 Solving 12.5 + P = -51.53882032 Solving for variable 'P'. Move all terms containing P to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + P = -51.53882032 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + P = -51.53882032 + -12.5 P = -51.53882032 + -12.5 Combine like terms: -51.53882032 + -12.5 = -64.03882032 P = -64.03882032 Simplifying P = -64.03882032Solution
The solution to the problem is based on the solutions from the subproblems. P = {39.03882032, -64.03882032}
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