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Simplifying u2 + -20u + 95 = 0 Reorder the terms: 95 + -20u + u2 = 0 Solving 95 + -20u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-95' to each side of the equation. 95 + -20u + -95 + u2 = 0 + -95 Reorder the terms: 95 + -95 + -20u + u2 = 0 + -95 Combine like terms: 95 + -95 = 0 0 + -20u + u2 = 0 + -95 -20u + u2 = 0 + -95 Combine like terms: 0 + -95 = -95 -20u + u2 = -95 The u term is -20u. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20u + 100 + u2 = -95 + 100 Reorder the terms: 100 + -20u + u2 = -95 + 100 Combine like terms: -95 + 100 = 5 100 + -20u + u2 = 5 Factor a perfect square on the left side: (u + -10)(u + -10) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (u + -10) equal to 2.236067978 and -2.236067978.Subproblem 1
u + -10 = 2.236067978 Simplifying u + -10 = 2.236067978 Reorder the terms: -10 + u = 2.236067978 Solving -10 + u = 2.236067978 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + u = 2.236067978 + 10 Combine like terms: -10 + 10 = 0 0 + u = 2.236067978 + 10 u = 2.236067978 + 10 Combine like terms: 2.236067978 + 10 = 12.236067978 u = 12.236067978 Simplifying u = 12.236067978Subproblem 2
u + -10 = -2.236067978 Simplifying u + -10 = -2.236067978 Reorder the terms: -10 + u = -2.236067978 Solving -10 + u = -2.236067978 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + u = -2.236067978 + 10 Combine like terms: -10 + 10 = 0 0 + u = -2.236067978 + 10 u = -2.236067978 + 10 Combine like terms: -2.236067978 + 10 = 7.763932022 u = 7.763932022 Simplifying u = 7.763932022Solution
The solution to the problem is based on the solutions from the subproblems. u = {12.236067978, 7.763932022}
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