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Simplifying -0.0333u2 + -0.4672u + 2.4573 = 0 Reorder the terms: 2.4573 + -0.4672u + -0.0333u2 = 0 Solving 2.4573 + -0.4672u + -0.0333u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -0.0333 the coefficient of the squared term: Divide each side by '-0.0333'. -73.79279279 + 14.03003003u + u2 = 0 Move the constant term to the right: Add '73.79279279' to each side of the equation. -73.79279279 + 14.03003003u + 73.79279279 + u2 = 0 + 73.79279279 Reorder the terms: -73.79279279 + 73.79279279 + 14.03003003u + u2 = 0 + 73.79279279 Combine like terms: -73.79279279 + 73.79279279 = 0.00000000 0.00000000 + 14.03003003u + u2 = 0 + 73.79279279 14.03003003u + u2 = 0 + 73.79279279 Combine like terms: 0 + 73.79279279 = 73.79279279 14.03003003u + u2 = 73.79279279 The u term is 14.03003003u. Take half its coefficient (7.015015015). Square it (49.21043566) and add it to both sides. Add '49.21043566' to each side of the equation. 14.03003003u + 49.21043566 + u2 = 73.79279279 + 49.21043566 Reorder the terms: 49.21043566 + 14.03003003u + u2 = 73.79279279 + 49.21043566 Combine like terms: 73.79279279 + 49.21043566 = 123.00322845 49.21043566 + 14.03003003u + u2 = 123.00322845 Factor a perfect square on the left side: (u + 7.015015015)(u + 7.015015015) = 123.00322845 Calculate the square root of the right side: 11.090682055 Break this problem into two subproblems by setting (u + 7.015015015) equal to 11.090682055 and -11.090682055.Subproblem 1
u + 7.015015015 = 11.090682055 Simplifying u + 7.015015015 = 11.090682055 Reorder the terms: 7.015015015 + u = 11.090682055 Solving 7.015015015 + u = 11.090682055 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-7.015015015' to each side of the equation. 7.015015015 + -7.015015015 + u = 11.090682055 + -7.015015015 Combine like terms: 7.015015015 + -7.015015015 = 0.000000000 0.000000000 + u = 11.090682055 + -7.015015015 u = 11.090682055 + -7.015015015 Combine like terms: 11.090682055 + -7.015015015 = 4.07566704 u = 4.07566704 Simplifying u = 4.07566704Subproblem 2
u + 7.015015015 = -11.090682055 Simplifying u + 7.015015015 = -11.090682055 Reorder the terms: 7.015015015 + u = -11.090682055 Solving 7.015015015 + u = -11.090682055 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-7.015015015' to each side of the equation. 7.015015015 + -7.015015015 + u = -11.090682055 + -7.015015015 Combine like terms: 7.015015015 + -7.015015015 = 0.000000000 0.000000000 + u = -11.090682055 + -7.015015015 u = -11.090682055 + -7.015015015 Combine like terms: -11.090682055 + -7.015015015 = -18.10569707 u = -18.10569707 Simplifying u = -18.10569707Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.07566704, -18.10569707}
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