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Simplifying (-2u2 + -7u + -1) + (8u2 + -5u + -4) = -1(-9u2 + 2u + -9) Reorder the terms: (-1 + -7u + -2u2) + (8u2 + -5u + -4) = -1(-9u2 + 2u + -9) Remove parenthesis around (-1 + -7u + -2u2) -1 + -7u + -2u2 + (8u2 + -5u + -4) = -1(-9u2 + 2u + -9) Reorder the terms: -1 + -7u + -2u2 + (-4 + -5u + 8u2) = -1(-9u2 + 2u + -9) Remove parenthesis around (-4 + -5u + 8u2) -1 + -7u + -2u2 + -4 + -5u + 8u2 = -1(-9u2 + 2u + -9) Reorder the terms: -1 + -4 + -7u + -5u + -2u2 + 8u2 = -1(-9u2 + 2u + -9) Combine like terms: -1 + -4 = -5 -5 + -7u + -5u + -2u2 + 8u2 = -1(-9u2 + 2u + -9) Combine like terms: -7u + -5u = -12u -5 + -12u + -2u2 + 8u2 = -1(-9u2 + 2u + -9) Combine like terms: -2u2 + 8u2 = 6u2 -5 + -12u + 6u2 = -1(-9u2 + 2u + -9) Reorder the terms: -5 + -12u + 6u2 = -1(-9 + 2u + -9u2) -5 + -12u + 6u2 = (-9 * -1 + 2u * -1 + -9u2 * -1) -5 + -12u + 6u2 = (9 + -2u + 9u2) Solving -5 + -12u + 6u2 = 9 + -2u + 9u2 Solving for variable 'u'. Reorder the terms: -5 + -9 + -12u + 2u + 6u2 + -9u2 = 9 + -2u + 9u2 + -9 + 2u + -9u2 Combine like terms: -5 + -9 = -14 -14 + -12u + 2u + 6u2 + -9u2 = 9 + -2u + 9u2 + -9 + 2u + -9u2 Combine like terms: -12u + 2u = -10u -14 + -10u + 6u2 + -9u2 = 9 + -2u + 9u2 + -9 + 2u + -9u2 Combine like terms: 6u2 + -9u2 = -3u2 -14 + -10u + -3u2 = 9 + -2u + 9u2 + -9 + 2u + -9u2 Reorder the terms: -14 + -10u + -3u2 = 9 + -9 + -2u + 2u + 9u2 + -9u2 Combine like terms: 9 + -9 = 0 -14 + -10u + -3u2 = 0 + -2u + 2u + 9u2 + -9u2 -14 + -10u + -3u2 = -2u + 2u + 9u2 + -9u2 Combine like terms: -2u + 2u = 0 -14 + -10u + -3u2 = 0 + 9u2 + -9u2 -14 + -10u + -3u2 = 9u2 + -9u2 Combine like terms: 9u2 + -9u2 = 0 -14 + -10u + -3u2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(14 + 10u + 3u2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(14 + 10u + 3u2)' equal to zero and attempt to solve: Simplifying 14 + 10u + 3u2 = 0 Solving 14 + 10u + 3u2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.666666667 + 3.333333333u + u2 = 0 Move the constant term to the right: Add '-4.666666667' to each side of the equation. 4.666666667 + 3.333333333u + -4.666666667 + u2 = 0 + -4.666666667 Reorder the terms: 4.666666667 + -4.666666667 + 3.333333333u + u2 = 0 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + 3.333333333u + u2 = 0 + -4.666666667 3.333333333u + u2 = 0 + -4.666666667 Combine like terms: 0 + -4.666666667 = -4.666666667 3.333333333u + u2 = -4.666666667 The u term is 3.333333333u. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333u + 2.777777779 + u2 = -4.666666667 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333u + u2 = -4.666666667 + 2.777777779 Combine like terms: -4.666666667 + 2.777777779 = -1.888888888 2.777777779 + 3.333333333u + u2 = -1.888888888 Factor a perfect square on the left side: (u + 1.666666667)(u + 1.666666667) = -1.888888888 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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