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Simplifying X2 + -1XP + XP + -1P2 = X2 + 2XP + P2 + -4P2 + -10P Reorder the terms: -1PX + PX + -1P2 + X2 = X2 + 2XP + P2 + -4P2 + -10P Combine like terms: -1PX + PX = 0 0 + -1P2 + X2 = X2 + 2XP + P2 + -4P2 + -10P -1P2 + X2 = X2 + 2XP + P2 + -4P2 + -10P Reorder the terms: -1P2 + X2 = -10P + 2PX + P2 + -4P2 + X2 Combine like terms: P2 + -4P2 = -3P2 -1P2 + X2 = -10P + 2PX + -3P2 + X2 Add '-1X2' to each side of the equation. -1P2 + X2 + -1X2 = -10P + 2PX + -3P2 + X2 + -1X2 Combine like terms: X2 + -1X2 = 0 -1P2 + 0 = -10P + 2PX + -3P2 + X2 + -1X2 -1P2 = -10P + 2PX + -3P2 + X2 + -1X2 Combine like terms: X2 + -1X2 = 0 -1P2 = -10P + 2PX + -3P2 + 0 -1P2 = -10P + 2PX + -3P2 Solving -1P2 = -10P + 2PX + -3P2 Solving for variable 'P'. Reorder the terms: 10P + -2PX + -1P2 + 3P2 = -10P + 2PX + -3P2 + 10P + -2PX + 3P2 Combine like terms: -1P2 + 3P2 = 2P2 10P + -2PX + 2P2 = -10P + 2PX + -3P2 + 10P + -2PX + 3P2 Reorder the terms: 10P + -2PX + 2P2 = -10P + 10P + 2PX + -2PX + -3P2 + 3P2 Combine like terms: -10P + 10P = 0 10P + -2PX + 2P2 = 0 + 2PX + -2PX + -3P2 + 3P2 10P + -2PX + 2P2 = 2PX + -2PX + -3P2 + 3P2 Combine like terms: 2PX + -2PX = 0 10P + -2PX + 2P2 = 0 + -3P2 + 3P2 10P + -2PX + 2P2 = -3P2 + 3P2 Combine like terms: -3P2 + 3P2 = 0 10P + -2PX + 2P2 = 0 Factor out the Greatest Common Factor (GCF), '2P'. 2P(5 + -1X + P) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'P' equal to zero and attempt to solve: Simplifying P = 0 Solving P = 0 Move all terms containing P to the left, all other terms to the right. Simplifying P = 0Subproblem 2
Set the factor '(5 + -1X + P)' equal to zero and attempt to solve: Simplifying 5 + -1X + P = 0 Reorder the terms: 5 + P + -1X = 0 Solving 5 + P + -1X = 0 Move all terms containing P to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + P + -5 + -1X = 0 + -5 Reorder the terms: 5 + -5 + P + -1X = 0 + -5 Combine like terms: 5 + -5 = 0 0 + P + -1X = 0 + -5 P + -1X = 0 + -5 Combine like terms: 0 + -5 = -5 P + -1X = -5 Add 'X' to each side of the equation. P + -1X + X = -5 + X Combine like terms: -1X + X = 0 P + 0 = -5 + X P = -5 + X Simplifying P = -5 + XSolution
P = {0, -5 + X}
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