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Simplifying (3u2 + -1u + 4) + (-5u2 + 6u + 7) = 0 Reorder the terms: (4 + -1u + 3u2) + (-5u2 + 6u + 7) = 0 Remove parenthesis around (4 + -1u + 3u2) 4 + -1u + 3u2 + (-5u2 + 6u + 7) = 0 Reorder the terms: 4 + -1u + 3u2 + (7 + 6u + -5u2) = 0 Remove parenthesis around (7 + 6u + -5u2) 4 + -1u + 3u2 + 7 + 6u + -5u2 = 0 Reorder the terms: 4 + 7 + -1u + 6u + 3u2 + -5u2 = 0 Combine like terms: 4 + 7 = 11 11 + -1u + 6u + 3u2 + -5u2 = 0 Combine like terms: -1u + 6u = 5u 11 + 5u + 3u2 + -5u2 = 0 Combine like terms: 3u2 + -5u2 = -2u2 11 + 5u + -2u2 = 0 Solving 11 + 5u + -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'. -5.5 + -2.5u + u2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -2.5u + 5.5 + u2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -2.5u + u2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -2.5u + u2 = 0 + 5.5 -2.5u + u2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -2.5u + u2 = 5.5 The u term is -2.5u. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5u + 1.5625 + u2 = 5.5 + 1.5625 Reorder the terms: 1.5625 + -2.5u + u2 = 5.5 + 1.5625 Combine like terms: 5.5 + 1.5625 = 7.0625 1.5625 + -2.5u + u2 = 7.0625 Factor a perfect square on the left side: (u + -1.25)(u + -1.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (u + -1.25) equal to 2.657536453 and -2.657536453.Subproblem 1
u + -1.25 = 2.657536453 Simplifying u + -1.25 = 2.657536453 Reorder the terms: -1.25 + u = 2.657536453 Solving -1.25 + u = 2.657536453 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + u = 2.657536453 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + u = 2.657536453 + 1.25 u = 2.657536453 + 1.25 Combine like terms: 2.657536453 + 1.25 = 3.907536453 u = 3.907536453 Simplifying u = 3.907536453Subproblem 2
u + -1.25 = -2.657536453 Simplifying u + -1.25 = -2.657536453 Reorder the terms: -1.25 + u = -2.657536453 Solving -1.25 + u = -2.657536453 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + u = -2.657536453 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + u = -2.657536453 + 1.25 u = -2.657536453 + 1.25 Combine like terms: -2.657536453 + 1.25 = -1.407536453 u = -1.407536453 Simplifying u = -1.407536453Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.907536453, -1.407536453}
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