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Simplifying 40 + -6u = u2 + -16 Reorder the terms: 40 + -6u = -16 + u2 Solving 40 + -6u = -16 + u2 Solving for variable 'u'. Reorder the terms: 40 + 16 + -6u + -1u2 = -16 + u2 + 16 + -1u2 Combine like terms: 40 + 16 = 56 56 + -6u + -1u2 = -16 + u2 + 16 + -1u2 Reorder the terms: 56 + -6u + -1u2 = -16 + 16 + u2 + -1u2 Combine like terms: -16 + 16 = 0 56 + -6u + -1u2 = 0 + u2 + -1u2 56 + -6u + -1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 56 + -6u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -56 + 6u + u2 = 0 Move the constant term to the right: Add '56' to each side of the equation. -56 + 6u + 56 + u2 = 0 + 56 Reorder the terms: -56 + 56 + 6u + u2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 6u + u2 = 0 + 56 6u + u2 = 0 + 56 Combine like terms: 0 + 56 = 56 6u + u2 = 56 The u term is 6u. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6u + 9 + u2 = 56 + 9 Reorder the terms: 9 + 6u + u2 = 56 + 9 Combine like terms: 56 + 9 = 65 9 + 6u + u2 = 65 Factor a perfect square on the left side: (u + 3)(u + 3) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (u + 3) equal to 8.062257748 and -8.062257748.Subproblem 1
u + 3 = 8.062257748 Simplifying u + 3 = 8.062257748 Reorder the terms: 3 + u = 8.062257748 Solving 3 + u = 8.062257748 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = 8.062257748 + -3 Combine like terms: 3 + -3 = 0 0 + u = 8.062257748 + -3 u = 8.062257748 + -3 Combine like terms: 8.062257748 + -3 = 5.062257748 u = 5.062257748 Simplifying u = 5.062257748Subproblem 2
u + 3 = -8.062257748 Simplifying u + 3 = -8.062257748 Reorder the terms: 3 + u = -8.062257748 Solving 3 + u = -8.062257748 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = -8.062257748 + -3 Combine like terms: 3 + -3 = 0 0 + u = -8.062257748 + -3 u = -8.062257748 + -3 Combine like terms: -8.062257748 + -3 = -11.062257748 u = -11.062257748 Simplifying u = -11.062257748Solution
The solution to the problem is based on the solutions from the subproblems. u = {5.062257748, -11.062257748}
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