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Simplifying u2 + -26u + -35 = 0 Reorder the terms: -35 + -26u + u2 = 0 Solving -35 + -26u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -26u + 35 + u2 = 0 + 35 Reorder the terms: -35 + 35 + -26u + u2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -26u + u2 = 0 + 35 -26u + u2 = 0 + 35 Combine like terms: 0 + 35 = 35 -26u + u2 = 35 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 = 35 + 169 Reorder the terms: 169 + -26u + u2 = 35 + 169 Combine like terms: 35 + 169 = 204 169 + -26u + u2 = 204 Factor a perfect square on the left side: (u + -13)(u + -13) = 204 Calculate the square root of the right side: 14.282856857 Break this problem into two subproblems by setting (u + -13) equal to 14.282856857 and -14.282856857.Subproblem 1
u + -13 = 14.282856857 Simplifying u + -13 = 14.282856857 Reorder the terms: -13 + u = 14.282856857 Solving -13 + u = 14.282856857 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 = 14.282856857 + 13 Combine like terms: -13 + 13 = 0 0 + u = 14.282856857 + 13 u = 14.282856857 + 13 Combine like terms: 14.282856857 + 13 = 27.282856857 u = 27.282856857 Simplifying u = 27.282856857Subproblem 2
u + -13 = -14.282856857 Simplifying u + -13 = -14.282856857 Reorder the terms: -13 + u = -14.282856857 Solving -13 + u = -14.282856857 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 = -14.282856857 + 13 Combine like terms: -13 + 13 = 0 0 + u = -14.282856857 + 13 u = -14.282856857 + 13 Combine like terms: -14.282856857 + 13 = -1.282856857 u = -1.282856857 Simplifying u = -1.282856857Solution
The solution to the problem is based on the solutions from the subproblems. u = {27.282856857, -1.282856857}
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