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Simplifying (-2u2 + 7u + -1) + (4u2 + 6u + 5) = 0 Reorder the terms: (-1 + 7u + -2u2) + (4u2 + 6u + 5) = 0 Remove parenthesis around (-1 + 7u + -2u2) -1 + 7u + -2u2 + (4u2 + 6u + 5) = 0 Reorder the terms: -1 + 7u + -2u2 + (5 + 6u + 4u2) = 0 Remove parenthesis around (5 + 6u + 4u2) -1 + 7u + -2u2 + 5 + 6u + 4u2 = 0 Reorder the terms: -1 + 5 + 7u + 6u + -2u2 + 4u2 = 0 Combine like terms: -1 + 5 = 4 4 + 7u + 6u + -2u2 + 4u2 = 0 Combine like terms: 7u + 6u = 13u 4 + 13u + -2u2 + 4u2 = 0 Combine like terms: -2u2 + 4u2 = 2u2 4 + 13u + 2u2 = 0 Solving 4 + 13u + 2u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + 6.5u + u2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 6.5u + -2 + u2 = 0 + -2 Reorder the terms: 2 + -2 + 6.5u + u2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 6.5u + u2 = 0 + -2 6.5u + u2 = 0 + -2 Combine like terms: 0 + -2 = -2 6.5u + u2 = -2 The u term is 6.5u. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5u + 10.5625 + u2 = -2 + 10.5625 Reorder the terms: 10.5625 + 6.5u + u2 = -2 + 10.5625 Combine like terms: -2 + 10.5625 = 8.5625 10.5625 + 6.5u + u2 = 8.5625 Factor a perfect square on the left side: (u + 3.25)(u + 3.25) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (u + 3.25) equal to 2.926174978 and -2.926174978.Subproblem 1
u + 3.25 = 2.926174978 Simplifying u + 3.25 = 2.926174978 Reorder the terms: 3.25 + u = 2.926174978 Solving 3.25 + u = 2.926174978 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + u = 2.926174978 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + u = 2.926174978 + -3.25 u = 2.926174978 + -3.25 Combine like terms: 2.926174978 + -3.25 = -0.323825022 u = -0.323825022 Simplifying u = -0.323825022Subproblem 2
u + 3.25 = -2.926174978 Simplifying u + 3.25 = -2.926174978 Reorder the terms: 3.25 + u = -2.926174978 Solving 3.25 + u = -2.926174978 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + u = -2.926174978 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + u = -2.926174978 + -3.25 u = -2.926174978 + -3.25 Combine like terms: -2.926174978 + -3.25 = -6.176174978 u = -6.176174978 Simplifying u = -6.176174978Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.323825022, -6.176174978}
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