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Simplifying 4u2 + 65u + -36 = 0 Reorder the terms: -36 + 65u + 4u2 = 0 Solving -36 + 65u + 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'. -9 + 16.25u + u2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 16.25u + 9 + u2 = 0 + 9 Reorder the terms: -9 + 9 + 16.25u + u2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 16.25u + u2 = 0 + 9 16.25u + u2 = 0 + 9 Combine like terms: 0 + 9 = 9 16.25u + u2 = 9 The u term is 16.25u. Take half its coefficient (8.125). Square it (66.015625) and add it to both sides. Add '66.015625' to each side of the equation. 16.25u + 66.015625 + u2 = 9 + 66.015625 Reorder the terms: 66.015625 + 16.25u + u2 = 9 + 66.015625 Combine like terms: 9 + 66.015625 = 75.015625 66.015625 + 16.25u + u2 = 75.015625 Factor a perfect square on the left side: (u + 8.125)(u + 8.125) = 75.015625 Calculate the square root of the right side: 8.661156101 Break this problem into two subproblems by setting (u + 8.125) equal to 8.661156101 and -8.661156101.Subproblem 1
u + 8.125 = 8.661156101 Simplifying u + 8.125 = 8.661156101 Reorder the terms: 8.125 + u = 8.661156101 Solving 8.125 + u = 8.661156101 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-8.125' to each side of the equation. 8.125 + -8.125 + u = 8.661156101 + -8.125 Combine like terms: 8.125 + -8.125 = 0.000 0.000 + u = 8.661156101 + -8.125 u = 8.661156101 + -8.125 Combine like terms: 8.661156101 + -8.125 = 0.536156101 u = 0.536156101 Simplifying u = 0.536156101Subproblem 2
u + 8.125 = -8.661156101 Simplifying u + 8.125 = -8.661156101 Reorder the terms: 8.125 + u = -8.661156101 Solving 8.125 + u = -8.661156101 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-8.125' to each side of the equation. 8.125 + -8.125 + u = -8.661156101 + -8.125 Combine like terms: 8.125 + -8.125 = 0.000 0.000 + u = -8.661156101 + -8.125 u = -8.661156101 + -8.125 Combine like terms: -8.661156101 + -8.125 = -16.786156101 u = -16.786156101 Simplifying u = -16.786156101Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.536156101, -16.786156101}
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