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Simplifying -3u2 + -23u + -13 = 0 Reorder the terms: -13 + -23u + -3u2 = 0 Solving -13 + -23u + -3u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 23u + 3u2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 23u + 3u2)' equal to zero and attempt to solve: Simplifying 13 + 23u + 3u2 = 0 Solving 13 + 23u + 3u2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.333333333 + 7.666666667u + u2 = 0 Move the constant term to the right: Add '-4.333333333' to each side of the equation. 4.333333333 + 7.666666667u + -4.333333333 + u2 = 0 + -4.333333333 Reorder the terms: 4.333333333 + -4.333333333 + 7.666666667u + u2 = 0 + -4.333333333 Combine like terms: 4.333333333 + -4.333333333 = 0.000000000 0.000000000 + 7.666666667u + u2 = 0 + -4.333333333 7.666666667u + u2 = 0 + -4.333333333 Combine like terms: 0 + -4.333333333 = -4.333333333 7.666666667u + u2 = -4.333333333 The u term is 7.666666667u. Take half its coefficient (3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. 7.666666667u + 14.69444445 + u2 = -4.333333333 + 14.69444445 Reorder the terms: 14.69444445 + 7.666666667u + u2 = -4.333333333 + 14.69444445 Combine like terms: -4.333333333 + 14.69444445 = 10.361111117 14.69444445 + 7.666666667u + u2 = 10.361111117 Factor a perfect square on the left side: (u + 3.833333334)(u + 3.833333334) = 10.361111117 Calculate the square root of the right side: 3.218867987 Break this problem into two subproblems by setting (u + 3.833333334) equal to 3.218867987 and -3.218867987.Subproblem 1
u + 3.833333334 = 3.218867987 Simplifying u + 3.833333334 = 3.218867987 Reorder the terms: 3.833333334 + u = 3.218867987 Solving 3.833333334 + u = 3.218867987 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3.833333334' to each side of the equation. 3.833333334 + -3.833333334 + u = 3.218867987 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + u = 3.218867987 + -3.833333334 u = 3.218867987 + -3.833333334 Combine like terms: 3.218867987 + -3.833333334 = -0.614465347 u = -0.614465347 Simplifying u = -0.614465347Subproblem 2
u + 3.833333334 = -3.218867987 Simplifying u + 3.833333334 = -3.218867987 Reorder the terms: 3.833333334 + u = -3.218867987 Solving 3.833333334 + u = -3.218867987 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3.833333334' to each side of the equation. 3.833333334 + -3.833333334 + u = -3.218867987 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + u = -3.218867987 + -3.833333334 u = -3.218867987 + -3.833333334 Combine like terms: -3.218867987 + -3.833333334 = -7.052201321 u = -7.052201321 Simplifying u = -7.052201321Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.614465347, -7.052201321}Solution
u = {-0.614465347, -7.052201321}
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