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Simplifying u2 + -26u + 27 = 0 Reorder the terms: 27 + -26u + u2 = 0 Solving 27 + -26u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -26u + -27 + u2 = 0 + -27 Reorder the terms: 27 + -27 + -26u + u2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -26u + u2 = 0 + -27 -26u + u2 = 0 + -27 Combine like terms: 0 + -27 = -27 -26u + u2 = -27 The u term is -26u. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26u + 169 + u2 = -27 + 169 Reorder the terms: 169 + -26u + u2 = -27 + 169 Combine like terms: -27 + 169 = 142 169 + -26u + u2 = 142 Factor a perfect square on the left side: (u + -13)(u + -13) = 142 Calculate the square root of the right side: 11.916375288 Break this problem into two subproblems by setting (u + -13) equal to 11.916375288 and -11.916375288.Subproblem 1
u + -13 = 11.916375288 Simplifying u + -13 = 11.916375288 Reorder the terms: -13 + u = 11.916375288 Solving -13 + u = 11.916375288 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + u = 11.916375288 + 13 Combine like terms: -13 + 13 = 0 0 + u = 11.916375288 + 13 u = 11.916375288 + 13 Combine like terms: 11.916375288 + 13 = 24.916375288 u = 24.916375288 Simplifying u = 24.916375288Subproblem 2
u + -13 = -11.916375288 Simplifying u + -13 = -11.916375288 Reorder the terms: -13 + u = -11.916375288 Solving -13 + u = -11.916375288 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + u = -11.916375288 + 13 Combine like terms: -13 + 13 = 0 0 + u = -11.916375288 + 13 u = -11.916375288 + 13 Combine like terms: -11.916375288 + 13 = 1.083624712 u = 1.083624712 Simplifying u = 1.083624712Solution
The solution to the problem is based on the solutions from the subproblems. u = {24.916375288, 1.083624712}
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