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Simplifying 3u2 = 14u + 15 Reorder the terms: 3u2 = 15 + 14u Solving 3u2 = 15 + 14u Solving for variable 'u'. Reorder the terms: -15 + -14u + 3u2 = 15 + 14u + -15 + -14u Reorder the terms: -15 + -14u + 3u2 = 15 + -15 + 14u + -14u Combine like terms: 15 + -15 = 0 -15 + -14u + 3u2 = 0 + 14u + -14u -15 + -14u + 3u2 = 14u + -14u Combine like terms: 14u + -14u = 0 -15 + -14u + 3u2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + -4.666666667u + u2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -4.666666667u + 5 + u2 = 0 + 5 Reorder the terms: -5 + 5 + -4.666666667u + u2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4.666666667u + u2 = 0 + 5 -4.666666667u + u2 = 0 + 5 Combine like terms: 0 + 5 = 5 -4.666666667u + u2 = 5 The u term is -4.666666667u. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667u + 5.444444448 + u2 = 5 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667u + u2 = 5 + 5.444444448 Combine like terms: 5 + 5.444444448 = 10.444444448 5.444444448 + -4.666666667u + u2 = 10.444444448 Factor a perfect square on the left side: (u + -2.333333334)(u + -2.333333334) = 10.444444448 Calculate the square root of the right side: 3.231786572 Break this problem into two subproblems by setting (u + -2.333333334) equal to 3.231786572 and -3.231786572.Subproblem 1
u + -2.333333334 = 3.231786572 Simplifying u + -2.333333334 = 3.231786572 Reorder the terms: -2.333333334 + u = 3.231786572 Solving -2.333333334 + u = 3.231786572 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + u = 3.231786572 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + u = 3.231786572 + 2.333333334 u = 3.231786572 + 2.333333334 Combine like terms: 3.231786572 + 2.333333334 = 5.565119906 u = 5.565119906 Simplifying u = 5.565119906Subproblem 2
u + -2.333333334 = -3.231786572 Simplifying u + -2.333333334 = -3.231786572 Reorder the terms: -2.333333334 + u = -3.231786572 Solving -2.333333334 + u = -3.231786572 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + u = -3.231786572 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + u = -3.231786572 + 2.333333334 u = -3.231786572 + 2.333333334 Combine like terms: -3.231786572 + 2.333333334 = -0.898453238 u = -0.898453238 Simplifying u = -0.898453238Solution
The solution to the problem is based on the solutions from the subproblems. u = {5.565119906, -0.898453238}
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