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Simplifying u2 + -2 = 2u2 + -10u + 16 Reorder the terms: -2 + u2 = 2u2 + -10u + 16 Reorder the terms: -2 + u2 = 16 + -10u + 2u2 Solving -2 + u2 = 16 + -10u + 2u2 Solving for variable 'u'. Reorder the terms: -2 + -16 + 10u + u2 + -2u2 = 16 + -10u + 2u2 + -16 + 10u + -2u2 Combine like terms: -2 + -16 = -18 -18 + 10u + u2 + -2u2 = 16 + -10u + 2u2 + -16 + 10u + -2u2 Combine like terms: u2 + -2u2 = -1u2 -18 + 10u + -1u2 = 16 + -10u + 2u2 + -16 + 10u + -2u2 Reorder the terms: -18 + 10u + -1u2 = 16 + -16 + -10u + 10u + 2u2 + -2u2 Combine like terms: 16 + -16 = 0 -18 + 10u + -1u2 = 0 + -10u + 10u + 2u2 + -2u2 -18 + 10u + -1u2 = -10u + 10u + 2u2 + -2u2 Combine like terms: -10u + 10u = 0 -18 + 10u + -1u2 = 0 + 2u2 + -2u2 -18 + 10u + -1u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 -18 + 10u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 18 + -10u + u2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -10u + -18 + u2 = 0 + -18 Reorder the terms: 18 + -18 + -10u + u2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -10u + u2 = 0 + -18 -10u + u2 = 0 + -18 Combine like terms: 0 + -18 = -18 -10u + u2 = -18 The u term is -10u. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10u + 25 + u2 = -18 + 25 Reorder the terms: 25 + -10u + u2 = -18 + 25 Combine like terms: -18 + 25 = 7 25 + -10u + u2 = 7 Factor a perfect square on the left side: (u + -5)(u + -5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (u + -5) equal to 2.645751311 and -2.645751311.Subproblem 1
u + -5 = 2.645751311 Simplifying u + -5 = 2.645751311 Reorder the terms: -5 + u = 2.645751311 Solving -5 + u = 2.645751311 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + u = 2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + u = 2.645751311 + 5 u = 2.645751311 + 5 Combine like terms: 2.645751311 + 5 = 7.645751311 u = 7.645751311 Simplifying u = 7.645751311Subproblem 2
u + -5 = -2.645751311 Simplifying u + -5 = -2.645751311 Reorder the terms: -5 + u = -2.645751311 Solving -5 + u = -2.645751311 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + u = -2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + u = -2.645751311 + 5 u = -2.645751311 + 5 Combine like terms: -2.645751311 + 5 = 2.354248689 u = 2.354248689 Simplifying u = 2.354248689Solution
The solution to the problem is based on the solutions from the subproblems. u = {7.645751311, 2.354248689}
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