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Simplifying u2 + -14u + 5 = 0 Reorder the terms: 5 + -14u + u2 = 0 Solving 5 + -14u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -14u + -5 + u2 = 0 + -5 Reorder the terms: 5 + -5 + -14u + u2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -14u + u2 = 0 + -5 -14u + u2 = 0 + -5 Combine like terms: 0 + -5 = -5 -14u + u2 = -5 The u term is -14u. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14u + 49 + u2 = -5 + 49 Reorder the terms: 49 + -14u + u2 = -5 + 49 Combine like terms: -5 + 49 = 44 49 + -14u + u2 = 44 Factor a perfect square on the left side: (u + -7)(u + -7) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (u + -7) equal to 6.633249581 and -6.633249581.Subproblem 1
u + -7 = 6.633249581 Simplifying u + -7 = 6.633249581 Reorder the terms: -7 + u = 6.633249581 Solving -7 + u = 6.633249581 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + u = 6.633249581 + 7 Combine like terms: -7 + 7 = 0 0 + u = 6.633249581 + 7 u = 6.633249581 + 7 Combine like terms: 6.633249581 + 7 = 13.633249581 u = 13.633249581 Simplifying u = 13.633249581Subproblem 2
u + -7 = -6.633249581 Simplifying u + -7 = -6.633249581 Reorder the terms: -7 + u = -6.633249581 Solving -7 + u = -6.633249581 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + u = -6.633249581 + 7 Combine like terms: -7 + 7 = 0 0 + u = -6.633249581 + 7 u = -6.633249581 + 7 Combine like terms: -6.633249581 + 7 = 0.366750419 u = 0.366750419 Simplifying u = 0.366750419Solution
The solution to the problem is based on the solutions from the subproblems. u = {13.633249581, 0.366750419}
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