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Simplifying u2 + -22u = -43 Reorder the terms: -22u + u2 = -43 Solving -22u + u2 = -43 Solving for variable 'u'. Reorder the terms: 43 + -22u + u2 = -43 + 43 Combine like terms: -43 + 43 = 0 43 + -22u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + -22u + -43 + u2 = 0 + -43 Reorder the terms: 43 + -43 + -22u + u2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + -22u + u2 = 0 + -43 -22u + u2 = 0 + -43 Combine like terms: 0 + -43 = -43 -22u + u2 = -43 The u term is -22u. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22u + 121 + u2 = -43 + 121 Reorder the terms: 121 + -22u + u2 = -43 + 121 Combine like terms: -43 + 121 = 78 121 + -22u + u2 = 78 Factor a perfect square on the left side: (u + -11)(u + -11) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (u + -11) equal to 8.831760866 and -8.831760866.Subproblem 1
u + -11 = 8.831760866 Simplifying u + -11 = 8.831760866 Reorder the terms: -11 + u = 8.831760866 Solving -11 + u = 8.831760866 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + u = 8.831760866 + 11 Combine like terms: -11 + 11 = 0 0 + u = 8.831760866 + 11 u = 8.831760866 + 11 Combine like terms: 8.831760866 + 11 = 19.831760866 u = 19.831760866 Simplifying u = 19.831760866Subproblem 2
u + -11 = -8.831760866 Simplifying u + -11 = -8.831760866 Reorder the terms: -11 + u = -8.831760866 Solving -11 + u = -8.831760866 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + u = -8.831760866 + 11 Combine like terms: -11 + 11 = 0 0 + u = -8.831760866 + 11 u = -8.831760866 + 11 Combine like terms: -8.831760866 + 11 = 2.168239134 u = 2.168239134 Simplifying u = 2.168239134Solution
The solution to the problem is based on the solutions from the subproblems. u = {19.831760866, 2.168239134}
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