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Simplifying u2 + -8u + -57 = 0 Reorder the terms: -57 + -8u + u2 = 0 Solving -57 + -8u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '57' to each side of the equation. -57 + -8u + 57 + u2 = 0 + 57 Reorder the terms: -57 + 57 + -8u + u2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + -8u + u2 = 0 + 57 -8u + u2 = 0 + 57 Combine like terms: 0 + 57 = 57 -8u + u2 = 57 The u term is -8u. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8u + 16 + u2 = 57 + 16 Reorder the terms: 16 + -8u + u2 = 57 + 16 Combine like terms: 57 + 16 = 73 16 + -8u + u2 = 73 Factor a perfect square on the left side: (u + -4)(u + -4) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (u + -4) equal to 8.544003745 and -8.544003745.Subproblem 1
u + -4 = 8.544003745 Simplifying u + -4 = 8.544003745 Reorder the terms: -4 + u = 8.544003745 Solving -4 + u = 8.544003745 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + u = 8.544003745 + 4 Combine like terms: -4 + 4 = 0 0 + u = 8.544003745 + 4 u = 8.544003745 + 4 Combine like terms: 8.544003745 + 4 = 12.544003745 u = 12.544003745 Simplifying u = 12.544003745Subproblem 2
u + -4 = -8.544003745 Simplifying u + -4 = -8.544003745 Reorder the terms: -4 + u = -8.544003745 Solving -4 + u = -8.544003745 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + u = -8.544003745 + 4 Combine like terms: -4 + 4 = 0 0 + u = -8.544003745 + 4 u = -8.544003745 + 4 Combine like terms: -8.544003745 + 4 = -4.544003745 u = -4.544003745 Simplifying u = -4.544003745Solution
The solution to the problem is based on the solutions from the subproblems. u = {12.544003745, -4.544003745}
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