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Simplifying u2 + -22u = -25 Reorder the terms: -22u + u2 = -25 Solving -22u + u2 = -25 Solving for variable 'u'. Reorder the terms: 25 + -22u + u2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + -22u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -22u + -25 + u2 = 0 + -25 Reorder the terms: 25 + -25 + -22u + u2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -22u + u2 = 0 + -25 -22u + u2 = 0 + -25 Combine like terms: 0 + -25 = -25 -22u + u2 = -25 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 = -25 + 121 Reorder the terms: 121 + -22u + u2 = -25 + 121 Combine like terms: -25 + 121 = 96 121 + -22u + u2 = 96 Factor a perfect square on the left side: (u + -11)(u + -11) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (u + -11) equal to 9.797958971 and -9.797958971.Subproblem 1
u + -11 = 9.797958971 Simplifying u + -11 = 9.797958971 Reorder the terms: -11 + u = 9.797958971 Solving -11 + u = 9.797958971 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 = 9.797958971 + 11 Combine like terms: -11 + 11 = 0 0 + u = 9.797958971 + 11 u = 9.797958971 + 11 Combine like terms: 9.797958971 + 11 = 20.797958971 u = 20.797958971 Simplifying u = 20.797958971Subproblem 2
u + -11 = -9.797958971 Simplifying u + -11 = -9.797958971 Reorder the terms: -11 + u = -9.797958971 Solving -11 + u = -9.797958971 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 = -9.797958971 + 11 Combine like terms: -11 + 11 = 0 0 + u = -9.797958971 + 11 u = -9.797958971 + 11 Combine like terms: -9.797958971 + 11 = 1.202041029 u = 1.202041029 Simplifying u = 1.202041029Solution
The solution to the problem is based on the solutions from the subproblems. u = {20.797958971, 1.202041029}
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