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Simplifying -0.0507u2 + -0.0949u + 1.1753 = 0 Reorder the terms: 1.1753 + -0.0949u + -0.0507u2 = 0 Solving 1.1753 + -0.0949u + -0.0507u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -0.0507 the coefficient of the squared term: Divide each side by '-0.0507'. -23.18145957 + 1.871794872u + u2 = 0 Move the constant term to the right: Add '23.18145957' to each side of the equation. -23.18145957 + 1.871794872u + 23.18145957 + u2 = 0 + 23.18145957 Reorder the terms: -23.18145957 + 23.18145957 + 1.871794872u + u2 = 0 + 23.18145957 Combine like terms: -23.18145957 + 23.18145957 = 0.00000000 0.00000000 + 1.871794872u + u2 = 0 + 23.18145957 1.871794872u + u2 = 0 + 23.18145957 Combine like terms: 0 + 23.18145957 = 23.18145957 1.871794872u + u2 = 23.18145957 The u term is 1.871794872u. Take half its coefficient (0.935897436). Square it (0.8759040107) and add it to both sides. Add '0.8759040107' to each side of the equation. 1.871794872u + 0.8759040107 + u2 = 23.18145957 + 0.8759040107 Reorder the terms: 0.8759040107 + 1.871794872u + u2 = 23.18145957 + 0.8759040107 Combine like terms: 23.18145957 + 0.8759040107 = 24.0573635807 0.8759040107 + 1.871794872u + u2 = 24.0573635807 Factor a perfect square on the left side: (u + 0.935897436)(u + 0.935897436) = 24.0573635807 Calculate the square root of the right side: 4.904830637 Break this problem into two subproblems by setting (u + 0.935897436) equal to 4.904830637 and -4.904830637.Subproblem 1
u + 0.935897436 = 4.904830637 Simplifying u + 0.935897436 = 4.904830637 Reorder the terms: 0.935897436 + u = 4.904830637 Solving 0.935897436 + u = 4.904830637 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.935897436' to each side of the equation. 0.935897436 + -0.935897436 + u = 4.904830637 + -0.935897436 Combine like terms: 0.935897436 + -0.935897436 = 0.000000000 0.000000000 + u = 4.904830637 + -0.935897436 u = 4.904830637 + -0.935897436 Combine like terms: 4.904830637 + -0.935897436 = 3.968933201 u = 3.968933201 Simplifying u = 3.968933201Subproblem 2
u + 0.935897436 = -4.904830637 Simplifying u + 0.935897436 = -4.904830637 Reorder the terms: 0.935897436 + u = -4.904830637 Solving 0.935897436 + u = -4.904830637 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.935897436' to each side of the equation. 0.935897436 + -0.935897436 + u = -4.904830637 + -0.935897436 Combine like terms: 0.935897436 + -0.935897436 = 0.000000000 0.000000000 + u = -4.904830637 + -0.935897436 u = -4.904830637 + -0.935897436 Combine like terms: -4.904830637 + -0.935897436 = -5.840728073 u = -5.840728073 Simplifying u = -5.840728073Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.968933201, -5.840728073}
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