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Simplifying u2 + 9 = 2u2 + 9u + -9 Reorder the terms: 9 + u2 = 2u2 + 9u + -9 Reorder the terms: 9 + u2 = -9 + 9u + 2u2 Solving 9 + u2 = -9 + 9u + 2u2 Solving for variable 'u'. Reorder the terms: 9 + 9 + -9u + u2 + -2u2 = -9 + 9u + 2u2 + 9 + -9u + -2u2 Combine like terms: 9 + 9 = 18 18 + -9u + u2 + -2u2 = -9 + 9u + 2u2 + 9 + -9u + -2u2 Combine like terms: u2 + -2u2 = -1u2 18 + -9u + -1u2 = -9 + 9u + 2u2 + 9 + -9u + -2u2 Reorder the terms: 18 + -9u + -1u2 = -9 + 9 + 9u + -9u + 2u2 + -2u2 Combine like terms: -9 + 9 = 0 18 + -9u + -1u2 = 0 + 9u + -9u + 2u2 + -2u2 18 + -9u + -1u2 = 9u + -9u + 2u2 + -2u2 Combine like terms: 9u + -9u = 0 18 + -9u + -1u2 = 0 + 2u2 + -2u2 18 + -9u + -1u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 18 + -9u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18 + 9u + u2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 9u + 18 + u2 = 0 + 18 Reorder the terms: -18 + 18 + 9u + u2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 9u + u2 = 0 + 18 9u + u2 = 0 + 18 Combine like terms: 0 + 18 = 18 9u + u2 = 18 The u term is 9u. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9u + 20.25 + u2 = 18 + 20.25 Reorder the terms: 20.25 + 9u + u2 = 18 + 20.25 Combine like terms: 18 + 20.25 = 38.25 20.25 + 9u + u2 = 38.25 Factor a perfect square on the left side: (u + 4.5)(u + 4.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (u + 4.5) equal to 6.184658438 and -6.184658438.Subproblem 1
u + 4.5 = 6.184658438 Simplifying u + 4.5 = 6.184658438 Reorder the terms: 4.5 + u = 6.184658438 Solving 4.5 + u = 6.184658438 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + u = 6.184658438 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + u = 6.184658438 + -4.5 u = 6.184658438 + -4.5 Combine like terms: 6.184658438 + -4.5 = 1.684658438 u = 1.684658438 Simplifying u = 1.684658438Subproblem 2
u + 4.5 = -6.184658438 Simplifying u + 4.5 = -6.184658438 Reorder the terms: 4.5 + u = -6.184658438 Solving 4.5 + u = -6.184658438 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + u = -6.184658438 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + u = -6.184658438 + -4.5 u = -6.184658438 + -4.5 Combine like terms: -6.184658438 + -4.5 = -10.684658438 u = -10.684658438 Simplifying u = -10.684658438Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.684658438, -10.684658438}
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