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Simplifying 3u2 + 26u + 15 = 0 Reorder the terms: 15 + 26u + 3u2 = 0 Solving 15 + 26u + 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'. 5 + 8.666666667u + u2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 8.666666667u + -5 + u2 = 0 + -5 Reorder the terms: 5 + -5 + 8.666666667u + u2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8.666666667u + u2 = 0 + -5 8.666666667u + u2 = 0 + -5 Combine like terms: 0 + -5 = -5 8.666666667u + u2 = -5 The u term is 8.666666667u. Take half its coefficient (4.333333334). Square it (18.77777778) and add it to both sides. Add '18.77777778' to each side of the equation. 8.666666667u + 18.77777778 + u2 = -5 + 18.77777778 Reorder the terms: 18.77777778 + 8.666666667u + u2 = -5 + 18.77777778 Combine like terms: -5 + 18.77777778 = 13.77777778 18.77777778 + 8.666666667u + u2 = 13.77777778 Factor a perfect square on the left side: (u + 4.333333334)(u + 4.333333334) = 13.77777778 Calculate the square root of the right side: 3.711842909 Break this problem into two subproblems by setting (u + 4.333333334) equal to 3.711842909 and -3.711842909.Subproblem 1
u + 4.333333334 = 3.711842909 Simplifying u + 4.333333334 = 3.711842909 Reorder the terms: 4.333333334 + u = 3.711842909 Solving 4.333333334 + u = 3.711842909 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.333333334' to each side of the equation. 4.333333334 + -4.333333334 + u = 3.711842909 + -4.333333334 Combine like terms: 4.333333334 + -4.333333334 = 0.000000000 0.000000000 + u = 3.711842909 + -4.333333334 u = 3.711842909 + -4.333333334 Combine like terms: 3.711842909 + -4.333333334 = -0.621490425 u = -0.621490425 Simplifying u = -0.621490425Subproblem 2
u + 4.333333334 = -3.711842909 Simplifying u + 4.333333334 = -3.711842909 Reorder the terms: 4.333333334 + u = -3.711842909 Solving 4.333333334 + u = -3.711842909 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.333333334' to each side of the equation. 4.333333334 + -4.333333334 + u = -3.711842909 + -4.333333334 Combine like terms: 4.333333334 + -4.333333334 = 0.000000000 0.000000000 + u = -3.711842909 + -4.333333334 u = -3.711842909 + -4.333333334 Combine like terms: -3.711842909 + -4.333333334 = -8.045176243 u = -8.045176243 Simplifying u = -8.045176243Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.621490425, -8.045176243}
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