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Simplifying u2 + -18u + 21 = 0 Reorder the terms: 21 + -18u + u2 = 0 Solving 21 + -18u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -18u + -21 + u2 = 0 + -21 Reorder the terms: 21 + -21 + -18u + u2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -18u + u2 = 0 + -21 -18u + u2 = 0 + -21 Combine like terms: 0 + -21 = -21 -18u + u2 = -21 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 = -21 + 81 Reorder the terms: 81 + -18u + u2 = -21 + 81 Combine like terms: -21 + 81 = 60 81 + -18u + u2 = 60 Factor a perfect square on the left side: (u + -9)(u + -9) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (u + -9) equal to 7.745966692 and -7.745966692.Subproblem 1
u + -9 = 7.745966692 Simplifying u + -9 = 7.745966692 Reorder the terms: -9 + u = 7.745966692 Solving -9 + u = 7.745966692 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 = 7.745966692 + 9 Combine like terms: -9 + 9 = 0 0 + u = 7.745966692 + 9 u = 7.745966692 + 9 Combine like terms: 7.745966692 + 9 = 16.745966692 u = 16.745966692 Simplifying u = 16.745966692Subproblem 2
u + -9 = -7.745966692 Simplifying u + -9 = -7.745966692 Reorder the terms: -9 + u = -7.745966692 Solving -9 + u = -7.745966692 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 = -7.745966692 + 9 Combine like terms: -9 + 9 = 0 0 + u = -7.745966692 + 9 u = -7.745966692 + 9 Combine like terms: -7.745966692 + 9 = 1.254033308 u = 1.254033308 Simplifying u = 1.254033308Solution
The solution to the problem is based on the solutions from the subproblems. u = {16.745966692, 1.254033308}
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