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Simplifying (2.5x2 + 0.2x + 2)(5x2 + 0.8x + 5) = 12 Reorder the terms: (2 + 0.2x + 2.5x2)(5x2 + 0.8x + 5) = 12 Reorder the terms: (2 + 0.2x + 2.5x2)(5 + 0.8x + 5x2) = 12 Multiply (2 + 0.2x + 2.5x2) * (5 + 0.8x + 5x2) (2(5 + 0.8x + 5x2) + 0.2x * (5 + 0.8x + 5x2) + 2.5x2 * (5 + 0.8x + 5x2)) = 12 ((5 * 2 + 0.8x * 2 + 5x2 * 2) + 0.2x * (5 + 0.8x + 5x2) + 2.5x2 * (5 + 0.8x + 5x2)) = 12 ((10 + 1.6x + 10x2) + 0.2x * (5 + 0.8x + 5x2) + 2.5x2 * (5 + 0.8x + 5x2)) = 12 (10 + 1.6x + 10x2 + (5 * 0.2x + 0.8x * 0.2x + 5x2 * 0.2x) + 2.5x2 * (5 + 0.8x + 5x2)) = 12 (10 + 1.6x + 10x2 + (1x + 0.16x2 + 1x3) + 2.5x2 * (5 + 0.8x + 5x2)) = 12 (10 + 1.6x + 10x2 + 1x + 0.16x2 + 1x3 + (5 * 2.5x2 + 0.8x * 2.5x2 + 5x2 * 2.5x2)) = 12 (10 + 1.6x + 10x2 + 1x + 0.16x2 + 1x3 + (12.5x2 + 2x3 + 12.5x4)) = 12 Reorder the terms: (10 + 1.6x + 1x + 10x2 + 0.16x2 + 12.5x2 + 1x3 + 2x3 + 12.5x4) = 12 Combine like terms: 1.6x + 1x = 2.6x (10 + 2.6x + 10x2 + 0.16x2 + 12.5x2 + 1x3 + 2x3 + 12.5x4) = 12 Combine like terms: 10x2 + 0.16x2 = 10.16x2 (10 + 2.6x + 10.16x2 + 12.5x2 + 1x3 + 2x3 + 12.5x4) = 12 Combine like terms: 10.16x2 + 12.5x2 = 22.66x2 (10 + 2.6x + 22.66x2 + 1x3 + 2x3 + 12.5x4) = 12 Combine like terms: 1x3 + 2x3 = 3x3 (10 + 2.6x + 22.66x2 + 3x3 + 12.5x4) = 12 Solving 10 + 2.6x + 22.66x2 + 3x3 + 12.5x4 = 12 Solving for variable 'x'. Reorder the terms: 10 + -12 + 2.6x + 22.66x2 + 3x3 + 12.5x4 = 12 + -12 Combine like terms: 10 + -12 = -2 -2 + 2.6x + 22.66x2 + 3x3 + 12.5x4 = 12 + -12 Combine like terms: 12 + -12 = 0 -2 + 2.6x + 22.66x2 + 3x3 + 12.5x4 = 0 The solution to this equation could not be determined.
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