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Simplifying 4u2 + -29u + -16 = 0 Reorder the terms: -16 + -29u + 4u2 = 0 Solving -16 + -29u + 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'. -4 + -7.25u + u2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -7.25u + 4 + u2 = 0 + 4 Reorder the terms: -4 + 4 + -7.25u + u2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7.25u + u2 = 0 + 4 -7.25u + u2 = 0 + 4 Combine like terms: 0 + 4 = 4 -7.25u + u2 = 4 The u term is -7.25u. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25u + 13.140625 + u2 = 4 + 13.140625 Reorder the terms: 13.140625 + -7.25u + u2 = 4 + 13.140625 Combine like terms: 4 + 13.140625 = 17.140625 13.140625 + -7.25u + u2 = 17.140625 Factor a perfect square on the left side: (u + -3.625)(u + -3.625) = 17.140625 Calculate the square root of the right side: 4.14012379 Break this problem into two subproblems by setting (u + -3.625) equal to 4.14012379 and -4.14012379.Subproblem 1
u + -3.625 = 4.14012379 Simplifying u + -3.625 = 4.14012379 Reorder the terms: -3.625 + u = 4.14012379 Solving -3.625 + u = 4.14012379 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + u = 4.14012379 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + u = 4.14012379 + 3.625 u = 4.14012379 + 3.625 Combine like terms: 4.14012379 + 3.625 = 7.76512379 u = 7.76512379 Simplifying u = 7.76512379Subproblem 2
u + -3.625 = -4.14012379 Simplifying u + -3.625 = -4.14012379 Reorder the terms: -3.625 + u = -4.14012379 Solving -3.625 + u = -4.14012379 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + u = -4.14012379 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + u = -4.14012379 + 3.625 u = -4.14012379 + 3.625 Combine like terms: -4.14012379 + 3.625 = -0.51512379 u = -0.51512379 Simplifying u = -0.51512379Solution
The solution to the problem is based on the solutions from the subproblems. u = {7.76512379, -0.51512379}
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