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Simplifying -6u2 + 7u = -52 Reorder the terms: 7u + -6u2 = -52 Solving 7u + -6u2 = -52 Solving for variable 'u'. Reorder the terms: 52 + 7u + -6u2 = -52 + 52 Combine like terms: -52 + 52 = 0 52 + 7u + -6u2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -8.666666667 + -1.166666667u + u2 = 0 Move the constant term to the right: Add '8.666666667' to each side of the equation. -8.666666667 + -1.166666667u + 8.666666667 + u2 = 0 + 8.666666667 Reorder the terms: -8.666666667 + 8.666666667 + -1.166666667u + u2 = 0 + 8.666666667 Combine like terms: -8.666666667 + 8.666666667 = 0.000000000 0.000000000 + -1.166666667u + u2 = 0 + 8.666666667 -1.166666667u + u2 = 0 + 8.666666667 Combine like terms: 0 + 8.666666667 = 8.666666667 -1.166666667u + u2 = 8.666666667 The u term is -1.166666667u. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667u + 0.3402777780 + u2 = 8.666666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667u + u2 = 8.666666667 + 0.3402777780 Combine like terms: 8.666666667 + 0.3402777780 = 9.006944445 0.3402777780 + -1.166666667u + u2 = 9.006944445 Factor a perfect square on the left side: (u + -0.5833333335)(u + -0.5833333335) = 9.006944445 Calculate the square root of the right side: 3.001157184 Break this problem into two subproblems by setting (u + -0.5833333335) equal to 3.001157184 and -3.001157184.Subproblem 1
u + -0.5833333335 = 3.001157184 Simplifying u + -0.5833333335 = 3.001157184 Reorder the terms: -0.5833333335 + u = 3.001157184 Solving -0.5833333335 + u = 3.001157184 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + u = 3.001157184 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + u = 3.001157184 + 0.5833333335 u = 3.001157184 + 0.5833333335 Combine like terms: 3.001157184 + 0.5833333335 = 3.5844905175 u = 3.5844905175 Simplifying u = 3.5844905175Subproblem 2
u + -0.5833333335 = -3.001157184 Simplifying u + -0.5833333335 = -3.001157184 Reorder the terms: -0.5833333335 + u = -3.001157184 Solving -0.5833333335 + u = -3.001157184 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + u = -3.001157184 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + u = -3.001157184 + 0.5833333335 u = -3.001157184 + 0.5833333335 Combine like terms: -3.001157184 + 0.5833333335 = -2.4178238505 u = -2.4178238505 Simplifying u = -2.4178238505Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.5844905175, -2.4178238505}
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