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Simplifying -2(5x + -5) + 3(4x + 2) + 10x(10x + 5) = 5(12x + 3) + 2x + -29 Reorder the terms: -2(-5 + 5x) + 3(4x + 2) + 10x(10x + 5) = 5(12x + 3) + 2x + -29 (-5 * -2 + 5x * -2) + 3(4x + 2) + 10x(10x + 5) = 5(12x + 3) + 2x + -29 (10 + -10x) + 3(4x + 2) + 10x(10x + 5) = 5(12x + 3) + 2x + -29 Reorder the terms: 10 + -10x + 3(2 + 4x) + 10x(10x + 5) = 5(12x + 3) + 2x + -29 10 + -10x + (2 * 3 + 4x * 3) + 10x(10x + 5) = 5(12x + 3) + 2x + -29 10 + -10x + (6 + 12x) + 10x(10x + 5) = 5(12x + 3) + 2x + -29 Reorder the terms: 10 + -10x + 6 + 12x + 10x(5 + 10x) = 5(12x + 3) + 2x + -29 10 + -10x + 6 + 12x + (5 * 10x + 10x * 10x) = 5(12x + 3) + 2x + -29 10 + -10x + 6 + 12x + (50x + 100x2) = 5(12x + 3) + 2x + -29 Reorder the terms: 10 + 6 + -10x + 12x + 50x + 100x2 = 5(12x + 3) + 2x + -29 Combine like terms: 10 + 6 = 16 16 + -10x + 12x + 50x + 100x2 = 5(12x + 3) + 2x + -29 Combine like terms: -10x + 12x = 2x 16 + 2x + 50x + 100x2 = 5(12x + 3) + 2x + -29 Combine like terms: 2x + 50x = 52x 16 + 52x + 100x2 = 5(12x + 3) + 2x + -29 Reorder the terms: 16 + 52x + 100x2 = 5(3 + 12x) + 2x + -29 16 + 52x + 100x2 = (3 * 5 + 12x * 5) + 2x + -29 16 + 52x + 100x2 = (15 + 60x) + 2x + -29 Reorder the terms: 16 + 52x + 100x2 = 15 + -29 + 60x + 2x Combine like terms: 15 + -29 = -14 16 + 52x + 100x2 = -14 + 60x + 2x Combine like terms: 60x + 2x = 62x 16 + 52x + 100x2 = -14 + 62x Solving 16 + 52x + 100x2 = -14 + 62x Solving for variable 'x'. Reorder the terms: 16 + 14 + 52x + -62x + 100x2 = -14 + 62x + 14 + -62x Combine like terms: 16 + 14 = 30 30 + 52x + -62x + 100x2 = -14 + 62x + 14 + -62x Combine like terms: 52x + -62x = -10x 30 + -10x + 100x2 = -14 + 62x + 14 + -62x Reorder the terms: 30 + -10x + 100x2 = -14 + 14 + 62x + -62x Combine like terms: -14 + 14 = 0 30 + -10x + 100x2 = 0 + 62x + -62x 30 + -10x + 100x2 = 62x + -62x Combine like terms: 62x + -62x = 0 30 + -10x + 100x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(3 + -1x + 10x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(3 + -1x + 10x2)' equal to zero and attempt to solve: Simplifying 3 + -1x + 10x2 = 0 Solving 3 + -1x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.3 + -0.1x + x2 = 0.0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + -0.1x + -0.3 + x2 = 0.0 + -0.3 Reorder the terms: 0.3 + -0.3 + -0.1x + x2 = 0.0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + -0.1x + x2 = 0.0 + -0.3 -0.1x + x2 = 0.0 + -0.3 Combine like terms: 0.0 + -0.3 = -0.3 -0.1x + x2 = -0.3 The x term is -0.1x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.1x + 0.0025 + x2 = -0.3 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = -0.3 + 0.0025 Combine like terms: -0.3 + 0.0025 = -0.2975 0.0025 + -0.1x + x2 = -0.2975 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = -0.2975 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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