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Simplifying u2 + -19u + 20 = 0 Reorder the terms: 20 + -19u + u2 = 0 Solving 20 + -19u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -19u + -20 + u2 = 0 + -20 Reorder the terms: 20 + -20 + -19u + u2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -19u + u2 = 0 + -20 -19u + u2 = 0 + -20 Combine like terms: 0 + -20 = -20 -19u + u2 = -20 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 = -20 + 90.25 Reorder the terms: 90.25 + -19u + u2 = -20 + 90.25 Combine like terms: -20 + 90.25 = 70.25 90.25 + -19u + u2 = 70.25 Factor a perfect square on the left side: (u + -9.5)(u + -9.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (u + -9.5) equal to 8.381527307 and -8.381527307.Subproblem 1
u + -9.5 = 8.381527307 Simplifying u + -9.5 = 8.381527307 Reorder the terms: -9.5 + u = 8.381527307 Solving -9.5 + u = 8.381527307 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 = 8.381527307 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + u = 8.381527307 + 9.5 u = 8.381527307 + 9.5 Combine like terms: 8.381527307 + 9.5 = 17.881527307 u = 17.881527307 Simplifying u = 17.881527307Subproblem 2
u + -9.5 = -8.381527307 Simplifying u + -9.5 = -8.381527307 Reorder the terms: -9.5 + u = -8.381527307 Solving -9.5 + u = -8.381527307 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 = -8.381527307 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + u = -8.381527307 + 9.5 u = -8.381527307 + 9.5 Combine like terms: -8.381527307 + 9.5 = 1.118472693 u = 1.118472693 Simplifying u = 1.118472693Solution
The solution to the problem is based on the solutions from the subproblems. u = {17.881527307, 1.118472693}
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