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Simplifying (u2 + -7u + -5) + (2u2 + -4u + 3) = 0 Reorder the terms: (-5 + -7u + u2) + (2u2 + -4u + 3) = 0 Remove parenthesis around (-5 + -7u + u2) -5 + -7u + u2 + (2u2 + -4u + 3) = 0 Reorder the terms: -5 + -7u + u2 + (3 + -4u + 2u2) = 0 Remove parenthesis around (3 + -4u + 2u2) -5 + -7u + u2 + 3 + -4u + 2u2 = 0 Reorder the terms: -5 + 3 + -7u + -4u + u2 + 2u2 = 0 Combine like terms: -5 + 3 = -2 -2 + -7u + -4u + u2 + 2u2 = 0 Combine like terms: -7u + -4u = -11u -2 + -11u + u2 + 2u2 = 0 Combine like terms: u2 + 2u2 = 3u2 -2 + -11u + 3u2 = 0 Solving -2 + -11u + 3u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -3.666666667u + u2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -3.666666667u + 0.6666666667 + u2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -3.666666667u + u2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -3.666666667u + u2 = 0 + 0.6666666667 -3.666666667u + u2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -3.666666667u + u2 = 0.6666666667 The u term is -3.666666667u. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667u + 3.361111114 + u2 = 0.6666666667 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667u + u2 = 0.6666666667 + 3.361111114 Combine like terms: 0.6666666667 + 3.361111114 = 4.0277777807 3.361111114 + -3.666666667u + u2 = 4.0277777807 Factor a perfect square on the left side: (u + -1.833333334)(u + -1.833333334) = 4.0277777807 Calculate the square root of the right side: 2.006932431 Break this problem into two subproblems by setting (u + -1.833333334) equal to 2.006932431 and -2.006932431.Subproblem 1
u + -1.833333334 = 2.006932431 Simplifying u + -1.833333334 = 2.006932431 Reorder the terms: -1.833333334 + u = 2.006932431 Solving -1.833333334 + u = 2.006932431 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + u = 2.006932431 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + u = 2.006932431 + 1.833333334 u = 2.006932431 + 1.833333334 Combine like terms: 2.006932431 + 1.833333334 = 3.840265765 u = 3.840265765 Simplifying u = 3.840265765Subproblem 2
u + -1.833333334 = -2.006932431 Simplifying u + -1.833333334 = -2.006932431 Reorder the terms: -1.833333334 + u = -2.006932431 Solving -1.833333334 + u = -2.006932431 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + u = -2.006932431 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + u = -2.006932431 + 1.833333334 u = -2.006932431 + 1.833333334 Combine like terms: -2.006932431 + 1.833333334 = -0.173599097 u = -0.173599097 Simplifying u = -0.173599097Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.840265765, -0.173599097}
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