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Simplifying u2 + -6u + -47 = 0 Reorder the terms: -47 + -6u + u2 = 0 Solving -47 + -6u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -6u + 47 + u2 = 0 + 47 Reorder the terms: -47 + 47 + -6u + u2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -6u + u2 = 0 + 47 -6u + u2 = 0 + 47 Combine like terms: 0 + 47 = 47 -6u + u2 = 47 The u term is -6u. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6u + 9 + u2 = 47 + 9 Reorder the terms: 9 + -6u + u2 = 47 + 9 Combine like terms: 47 + 9 = 56 9 + -6u + u2 = 56 Factor a perfect square on the left side: (u + -3)(u + -3) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (u + -3) equal to 7.483314774 and -7.483314774.Subproblem 1
u + -3 = 7.483314774 Simplifying u + -3 = 7.483314774 Reorder the terms: -3 + u = 7.483314774 Solving -3 + u = 7.483314774 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + u = 7.483314774 + 3 Combine like terms: -3 + 3 = 0 0 + u = 7.483314774 + 3 u = 7.483314774 + 3 Combine like terms: 7.483314774 + 3 = 10.483314774 u = 10.483314774 Simplifying u = 10.483314774Subproblem 2
u + -3 = -7.483314774 Simplifying u + -3 = -7.483314774 Reorder the terms: -3 + u = -7.483314774 Solving -3 + u = -7.483314774 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + u = -7.483314774 + 3 Combine like terms: -3 + 3 = 0 0 + u = -7.483314774 + 3 u = -7.483314774 + 3 Combine like terms: -7.483314774 + 3 = -4.483314774 u = -4.483314774 Simplifying u = -4.483314774Solution
The solution to the problem is based on the solutions from the subproblems. u = {10.483314774, -4.483314774}
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