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Simplifying 6u2 + 25u + 23 = 0 Reorder the terms: 23 + 25u + 6u2 = 0 Solving 23 + 25u + 6u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 3.833333333 + 4.166666667u + u2 = 0 Move the constant term to the right: Add '-3.833333333' to each side of the equation. 3.833333333 + 4.166666667u + -3.833333333 + u2 = 0 + -3.833333333 Reorder the terms: 3.833333333 + -3.833333333 + 4.166666667u + u2 = 0 + -3.833333333 Combine like terms: 3.833333333 + -3.833333333 = 0.000000000 0.000000000 + 4.166666667u + u2 = 0 + -3.833333333 4.166666667u + u2 = 0 + -3.833333333 Combine like terms: 0 + -3.833333333 = -3.833333333 4.166666667u + u2 = -3.833333333 The u term is 4.166666667u. Take half its coefficient (2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. 4.166666667u + 4.340277781 + u2 = -3.833333333 + 4.340277781 Reorder the terms: 4.340277781 + 4.166666667u + u2 = -3.833333333 + 4.340277781 Combine like terms: -3.833333333 + 4.340277781 = 0.506944448 4.340277781 + 4.166666667u + u2 = 0.506944448 Factor a perfect square on the left side: (u + 2.083333334)(u + 2.083333334) = 0.506944448 Calculate the square root of the right side: 0.712000315 Break this problem into two subproblems by setting (u + 2.083333334) equal to 0.712000315 and -0.712000315.Subproblem 1
u + 2.083333334 = 0.712000315 Simplifying u + 2.083333334 = 0.712000315 Reorder the terms: 2.083333334 + u = 0.712000315 Solving 2.083333334 + u = 0.712000315 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + u = 0.712000315 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + u = 0.712000315 + -2.083333334 u = 0.712000315 + -2.083333334 Combine like terms: 0.712000315 + -2.083333334 = -1.371333019 u = -1.371333019 Simplifying u = -1.371333019Subproblem 2
u + 2.083333334 = -0.712000315 Simplifying u + 2.083333334 = -0.712000315 Reorder the terms: 2.083333334 + u = -0.712000315 Solving 2.083333334 + u = -0.712000315 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + u = -0.712000315 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + u = -0.712000315 + -2.083333334 u = -0.712000315 + -2.083333334 Combine like terms: -0.712000315 + -2.083333334 = -2.795333649 u = -2.795333649 Simplifying u = -2.795333649Solution
The solution to the problem is based on the solutions from the subproblems. u = {-1.371333019, -2.795333649}
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