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Simplifying (3u2 + -3u + -9) + (8u2 + 9u + 9) + -1(6u2 + -8u + -7) = 0 Reorder the terms: (-9 + -3u + 3u2) + (8u2 + 9u + 9) + -1(6u2 + -8u + -7) = 0 Remove parenthesis around (-9 + -3u + 3u2) -9 + -3u + 3u2 + (8u2 + 9u + 9) + -1(6u2 + -8u + -7) = 0 Reorder the terms: -9 + -3u + 3u2 + (9 + 9u + 8u2) + -1(6u2 + -8u + -7) = 0 Remove parenthesis around (9 + 9u + 8u2) -9 + -3u + 3u2 + 9 + 9u + 8u2 + -1(6u2 + -8u + -7) = 0 Reorder the terms: -9 + -3u + 3u2 + 9 + 9u + 8u2 + -1(-7 + -8u + 6u2) = 0 -9 + -3u + 3u2 + 9 + 9u + 8u2 + (-7 * -1 + -8u * -1 + 6u2 * -1) = 0 -9 + -3u + 3u2 + 9 + 9u + 8u2 + (7 + 8u + -6u2) = 0 Reorder the terms: -9 + 9 + 7 + -3u + 9u + 8u + 3u2 + 8u2 + -6u2 = 0 Combine like terms: -9 + 9 = 0 0 + 7 + -3u + 9u + 8u + 3u2 + 8u2 + -6u2 = 0 7 + -3u + 9u + 8u + 3u2 + 8u2 + -6u2 = 0 Combine like terms: -3u + 9u = 6u 7 + 6u + 8u + 3u2 + 8u2 + -6u2 = 0 Combine like terms: 6u + 8u = 14u 7 + 14u + 3u2 + 8u2 + -6u2 = 0 Combine like terms: 3u2 + 8u2 = 11u2 7 + 14u + 11u2 + -6u2 = 0 Combine like terms: 11u2 + -6u2 = 5u2 7 + 14u + 5u2 = 0 Solving 7 + 14u + 5u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + 2.8u + u2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 2.8u + -1.4 + u2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 2.8u + u2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 2.8u + u2 = 0 + -1.4 2.8u + u2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 2.8u + u2 = -1.4 The u term is 2.8u. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8u + 1.96 + u2 = -1.4 + 1.96 Reorder the terms: 1.96 + 2.8u + u2 = -1.4 + 1.96 Combine like terms: -1.4 + 1.96 = 0.56 1.96 + 2.8u + u2 = 0.56 Factor a perfect square on the left side: (u + 1.4)(u + 1.4) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (u + 1.4) equal to 0.748331477 and -0.748331477.Subproblem 1
u + 1.4 = 0.748331477 Simplifying u + 1.4 = 0.748331477 Reorder the terms: 1.4 + u = 0.748331477 Solving 1.4 + u = 0.748331477 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + u = 0.748331477 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + u = 0.748331477 + -1.4 u = 0.748331477 + -1.4 Combine like terms: 0.748331477 + -1.4 = -0.651668523 u = -0.651668523 Simplifying u = -0.651668523Subproblem 2
u + 1.4 = -0.748331477 Simplifying u + 1.4 = -0.748331477 Reorder the terms: 1.4 + u = -0.748331477 Solving 1.4 + u = -0.748331477 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + u = -0.748331477 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + u = -0.748331477 + -1.4 u = -0.748331477 + -1.4 Combine like terms: -0.748331477 + -1.4 = -2.148331477 u = -2.148331477 Simplifying u = -2.148331477Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.651668523, -2.148331477}
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