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Simplifying (1 + -1x)(1 + -0.5X) * 50 + (1 + -1x)(1 + -0.3x) * 60 = 0 Reorder the terms for easier multiplication: 50(1 + -1x)(1 + -0.5X) + (1 + -1x)(1 + -0.3x) * 60 = 0 Multiply (1 + -1x) * (1 + -0.5X) 50(1(1 + -0.5X) + -1x * (1 + -0.5X)) + (1 + -1x)(1 + -0.3x) * 60 = 0 50((1 * 1 + -0.5X * 1) + -1x * (1 + -0.5X)) + (1 + -1x)(1 + -0.3x) * 60 = 0 50((1 + -0.5X) + -1x * (1 + -0.5X)) + (1 + -1x)(1 + -0.3x) * 60 = 0 50(1 + -0.5X + (1 * -1x + -0.5X * -1x)) + (1 + -1x)(1 + -0.3x) * 60 = 0 50(1 + -0.5X + (-1x + 0.5xX)) + (1 + -1x)(1 + -0.3x) * 60 = 0 50(1 + -0.5X + -1x + 0.5xX) + (1 + -1x)(1 + -0.3x) * 60 = 0 (1 * 50 + -0.5X * 50 + -1x * 50 + 0.5xX * 50) + (1 + -1x)(1 + -0.3x) * 60 = 0 (50 + -25X + -50x + 25xX) + (1 + -1x)(1 + -0.3x) * 60 = 0 Reorder the terms for easier multiplication: 50 + -25X + -50x + 25xX + 60(1 + -1x)(1 + -0.3x) = 0 Multiply (1 + -1x) * (1 + -0.3x) 50 + -25X + -50x + 25xX + 60(1(1 + -0.3x) + -1x * (1 + -0.3x)) = 0 50 + -25X + -50x + 25xX + 60((1 * 1 + -0.3x * 1) + -1x * (1 + -0.3x)) = 0 50 + -25X + -50x + 25xX + 60((1 + -0.3x) + -1x * (1 + -0.3x)) = 0 50 + -25X + -50x + 25xX + 60(1 + -0.3x + (1 * -1x + -0.3x * -1x)) = 0 50 + -25X + -50x + 25xX + 60(1 + -0.3x + (-1x + 0.3x2)) = 0 Combine like terms: -0.3x + -1x = -1.3x 50 + -25X + -50x + 25xX + 60(1 + -1.3x + 0.3x2) = 0 50 + -25X + -50x + 25xX + (1 * 60 + -1.3x * 60 + 0.3x2 * 60) = 0 50 + -25X + -50x + 25xX + (60 + -78x + 18x2) = 0 Reorder the terms: 50 + 60 + -25X + -50x + -78x + 25xX + 18x2 = 0 Combine like terms: 50 + 60 = 110 110 + -25X + -50x + -78x + 25xX + 18x2 = 0 Combine like terms: -50x + -78x = -128x 110 + -25X + -128x + 25xX + 18x2 = 0 Solving 110 + -25X + -128x + 25xX + 18x2 = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-110' to each side of the equation. 110 + -25X + -128x + 25xX + -110 + 18x2 = 0 + -110 Reorder the terms: 110 + -110 + -25X + -128x + 25xX + 18x2 = 0 + -110 Combine like terms: 110 + -110 = 0 0 + -25X + -128x + 25xX + 18x2 = 0 + -110 -25X + -128x + 25xX + 18x2 = 0 + -110 Combine like terms: 0 + -110 = -110 -25X + -128x + 25xX + 18x2 = -110 Add '128x' to each side of the equation. -25X + -128x + 25xX + 128x + 18x2 = -110 + 128x Reorder the terms: -25X + -128x + 128x + 25xX + 18x2 = -110 + 128x Combine like terms: -128x + 128x = 0 -25X + 0 + 25xX + 18x2 = -110 + 128x -25X + 25xX + 18x2 = -110 + 128x Add '-18x2' to each side of the equation. -25X + 25xX + 18x2 + -18x2 = -110 + 128x + -18x2 Combine like terms: 18x2 + -18x2 = 0 -25X + 25xX + 0 = -110 + 128x + -18x2 -25X + 25xX = -110 + 128x + -18x2 Reorder the terms: 110 + -25X + -128x + 25xX + 18x2 = -110 + 128x + -18x2 + 110 + -128x + 18x2 Reorder the terms: 110 + -25X + -128x + 25xX + 18x2 = -110 + 110 + 128x + -128x + -18x2 + 18x2 Combine like terms: -110 + 110 = 0 110 + -25X + -128x + 25xX + 18x2 = 0 + 128x + -128x + -18x2 + 18x2 110 + -25X + -128x + 25xX + 18x2 = 128x + -128x + -18x2 + 18x2 Combine like terms: 128x + -128x = 0 110 + -25X + -128x + 25xX + 18x2 = 0 + -18x2 + 18x2 110 + -25X + -128x + 25xX + 18x2 = -18x2 + 18x2 Combine like terms: -18x2 + 18x2 = 0 110 + -25X + -128x + 25xX + 18x2 = 0 The solution to this equation could not be determined.
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