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