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Simplifying 0 = u2 + -18u + 9 Reorder the terms: 0 = 9 + -18u + u2 Solving 0 = 9 + -18u + u2 Solving for variable 'u'. Combine like terms: 0 + -9 = -9 -9 + 18u + -1u2 = 9 + -18u + u2 + -9 + 18u + -1u2 Reorder the terms: -9 + 18u + -1u2 = 9 + -9 + -18u + 18u + u2 + -1u2 Combine like terms: 9 + -9 = 0 -9 + 18u + -1u2 = 0 + -18u + 18u + u2 + -1u2 -9 + 18u + -1u2 = -18u + 18u + u2 + -1u2 Combine like terms: -18u + 18u = 0 -9 + 18u + -1u2 = 0 + u2 + -1u2 -9 + 18u + -1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 -9 + 18u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 9 + -18u + u2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -18u + -9 + u2 = 0 + -9 Reorder the terms: 9 + -9 + -18u + u2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -18u + u2 = 0 + -9 -18u + u2 = 0 + -9 Combine like terms: 0 + -9 = -9 -18u + u2 = -9 The u term is -18u. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18u + 81 + u2 = -9 + 81 Reorder the terms: 81 + -18u + u2 = -9 + 81 Combine like terms: -9 + 81 = 72 81 + -18u + u2 = 72 Factor a perfect square on the left side: (u + -9)(u + -9) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (u + -9) equal to 8.485281374 and -8.485281374.Subproblem 1
u + -9 = 8.485281374 Simplifying u + -9 = 8.485281374 Reorder the terms: -9 + u = 8.485281374 Solving -9 + u = 8.485281374 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + u = 8.485281374 + 9 Combine like terms: -9 + 9 = 0 0 + u = 8.485281374 + 9 u = 8.485281374 + 9 Combine like terms: 8.485281374 + 9 = 17.485281374 u = 17.485281374 Simplifying u = 17.485281374Subproblem 2
u + -9 = -8.485281374 Simplifying u + -9 = -8.485281374 Reorder the terms: -9 + u = -8.485281374 Solving -9 + u = -8.485281374 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + u = -8.485281374 + 9 Combine like terms: -9 + 9 = 0 0 + u = -8.485281374 + 9 u = -8.485281374 + 9 Combine like terms: -8.485281374 + 9 = 0.514718626 u = 0.514718626 Simplifying u = 0.514718626Solution
The solution to the problem is based on the solutions from the subproblems. u = {17.485281374, 0.514718626}
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