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Simplifying 128 + -16u + -1u2 = 0 Solving 128 + -16u + -1u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -128 + 16u + u2 = 0 Move the constant term to the right: Add '128' to each side of the equation. -128 + 16u + 128 + u2 = 0 + 128 Reorder the terms: -128 + 128 + 16u + u2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 16u + u2 = 0 + 128 16u + u2 = 0 + 128 Combine like terms: 0 + 128 = 128 16u + u2 = 128 The u term is 16u. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16u + 64 + u2 = 128 + 64 Reorder the terms: 64 + 16u + u2 = 128 + 64 Combine like terms: 128 + 64 = 192 64 + 16u + u2 = 192 Factor a perfect square on the left side: (u + 8)(u + 8) = 192 Calculate the square root of the right side: 13.856406461 Break this problem into two subproblems by setting (u + 8) equal to 13.856406461 and -13.856406461.Subproblem 1
u + 8 = 13.856406461 Simplifying u + 8 = 13.856406461 Reorder the terms: 8 + u = 13.856406461 Solving 8 + u = 13.856406461 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + u = 13.856406461 + -8 Combine like terms: 8 + -8 = 0 0 + u = 13.856406461 + -8 u = 13.856406461 + -8 Combine like terms: 13.856406461 + -8 = 5.856406461 u = 5.856406461 Simplifying u = 5.856406461Subproblem 2
u + 8 = -13.856406461 Simplifying u + 8 = -13.856406461 Reorder the terms: 8 + u = -13.856406461 Solving 8 + u = -13.856406461 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + u = -13.856406461 + -8 Combine like terms: 8 + -8 = 0 0 + u = -13.856406461 + -8 u = -13.856406461 + -8 Combine like terms: -13.856406461 + -8 = -21.856406461 u = -21.856406461 Simplifying u = -21.856406461Solution
The solution to the problem is based on the solutions from the subproblems. u = {5.856406461, -21.856406461}
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