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Simplifying u2 + -14u + 8 = 0 Reorder the terms: 8 + -14u + u2 = 0 Solving 8 + -14u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -14u + -8 + u2 = 0 + -8 Reorder the terms: 8 + -8 + -14u + u2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -14u + u2 = 0 + -8 -14u + u2 = 0 + -8 Combine like terms: 0 + -8 = -8 -14u + u2 = -8 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 = -8 + 49 Reorder the terms: 49 + -14u + u2 = -8 + 49 Combine like terms: -8 + 49 = 41 49 + -14u + u2 = 41 Factor a perfect square on the left side: (u + -7)(u + -7) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (u + -7) equal to 6.403124237 and -6.403124237.Subproblem 1
u + -7 = 6.403124237 Simplifying u + -7 = 6.403124237 Reorder the terms: -7 + u = 6.403124237 Solving -7 + u = 6.403124237 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 = 6.403124237 + 7 Combine like terms: -7 + 7 = 0 0 + u = 6.403124237 + 7 u = 6.403124237 + 7 Combine like terms: 6.403124237 + 7 = 13.403124237 u = 13.403124237 Simplifying u = 13.403124237Subproblem 2
u + -7 = -6.403124237 Simplifying u + -7 = -6.403124237 Reorder the terms: -7 + u = -6.403124237 Solving -7 + u = -6.403124237 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 = -6.403124237 + 7 Combine like terms: -7 + 7 = 0 0 + u = -6.403124237 + 7 u = -6.403124237 + 7 Combine like terms: -6.403124237 + 7 = 0.596875763 u = 0.596875763 Simplifying u = 0.596875763Solution
The solution to the problem is based on the solutions from the subproblems. u = {13.403124237, 0.596875763}
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