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Simplifying u2 + 19u + -46 = 0 Reorder the terms: -46 + 19u + u2 = 0 Solving -46 + 19u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 19u + 46 + u2 = 0 + 46 Reorder the terms: -46 + 46 + 19u + u2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 19u + u2 = 0 + 46 19u + u2 = 0 + 46 Combine like terms: 0 + 46 = 46 19u + u2 = 46 The u term is 19u. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19u + 90.25 + u2 = 46 + 90.25 Reorder the terms: 90.25 + 19u + u2 = 46 + 90.25 Combine like terms: 46 + 90.25 = 136.25 90.25 + 19u + u2 = 136.25 Factor a perfect square on the left side: (u + 9.5)(u + 9.5) = 136.25 Calculate the square root of the right side: 11.67261753 Break this problem into two subproblems by setting (u + 9.5) equal to 11.67261753 and -11.67261753.Subproblem 1
u + 9.5 = 11.67261753 Simplifying u + 9.5 = 11.67261753 Reorder the terms: 9.5 + u = 11.67261753 Solving 9.5 + u = 11.67261753 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + u = 11.67261753 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + u = 11.67261753 + -9.5 u = 11.67261753 + -9.5 Combine like terms: 11.67261753 + -9.5 = 2.17261753 u = 2.17261753 Simplifying u = 2.17261753Subproblem 2
u + 9.5 = -11.67261753 Simplifying u + 9.5 = -11.67261753 Reorder the terms: 9.5 + u = -11.67261753 Solving 9.5 + u = -11.67261753 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + u = -11.67261753 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + u = -11.67261753 + -9.5 u = -11.67261753 + -9.5 Combine like terms: -11.67261753 + -9.5 = -21.17261753 u = -21.17261753 Simplifying u = -21.17261753Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.17261753, -21.17261753}
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