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Simplifying 4u2 + -11u + 1 = 0 Reorder the terms: 1 + -11u + 4u2 = 0 Solving 1 + -11u + 4u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + -2.75u + u2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -2.75u + -0.25 + u2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -2.75u + u2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -2.75u + u2 = 0 + -0.25 -2.75u + u2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -2.75u + u2 = -0.25 The u term is -2.75u. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75u + 1.890625 + u2 = -0.25 + 1.890625 Reorder the terms: 1.890625 + -2.75u + u2 = -0.25 + 1.890625 Combine like terms: -0.25 + 1.890625 = 1.640625 1.890625 + -2.75u + u2 = 1.640625 Factor a perfect square on the left side: (u + -1.375)(u + -1.375) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (u + -1.375) equal to 1.280868846 and -1.280868846.Subproblem 1
u + -1.375 = 1.280868846 Simplifying u + -1.375 = 1.280868846 Reorder the terms: -1.375 + u = 1.280868846 Solving -1.375 + u = 1.280868846 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + u = 1.280868846 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + u = 1.280868846 + 1.375 u = 1.280868846 + 1.375 Combine like terms: 1.280868846 + 1.375 = 2.655868846 u = 2.655868846 Simplifying u = 2.655868846Subproblem 2
u + -1.375 = -1.280868846 Simplifying u + -1.375 = -1.280868846 Reorder the terms: -1.375 + u = -1.280868846 Solving -1.375 + u = -1.280868846 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + u = -1.280868846 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + u = -1.280868846 + 1.375 u = -1.280868846 + 1.375 Combine like terms: -1.280868846 + 1.375 = 0.094131154 u = 0.094131154 Simplifying u = 0.094131154Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.655868846, 0.094131154}
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