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Simplifying -0.0525u2 + -0.1552u + 1.5383 = 0 Reorder the terms: 1.5383 + -0.1552u + -0.0525u2 = 0 Solving 1.5383 + -0.1552u + -0.0525u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -0.0525 the coefficient of the squared term: Divide each side by '-0.0525'. -29.30095238 + 2.956190476u + u2 = 0 Move the constant term to the right: Add '29.30095238' to each side of the equation. -29.30095238 + 2.956190476u + 29.30095238 + u2 = 0 + 29.30095238 Reorder the terms: -29.30095238 + 29.30095238 + 2.956190476u + u2 = 0 + 29.30095238 Combine like terms: -29.30095238 + 29.30095238 = 0.00000000 0.00000000 + 2.956190476u + u2 = 0 + 29.30095238 2.956190476u + u2 = 0 + 29.30095238 Combine like terms: 0 + 29.30095238 = 29.30095238 2.956190476u + u2 = 29.30095238 The u term is 2.956190476u. Take half its coefficient (1.478095238). Square it (2.184765533) and add it to both sides. Add '2.184765533' to each side of the equation. 2.956190476u + 2.184765533 + u2 = 29.30095238 + 2.184765533 Reorder the terms: 2.184765533 + 2.956190476u + u2 = 29.30095238 + 2.184765533 Combine like terms: 29.30095238 + 2.184765533 = 31.485717913 2.184765533 + 2.956190476u + u2 = 31.485717913 Factor a perfect square on the left side: (u + 1.478095238)(u + 1.478095238) = 31.485717913 Calculate the square root of the right side: 5.611213586 Break this problem into two subproblems by setting (u + 1.478095238) equal to 5.611213586 and -5.611213586.Subproblem 1
u + 1.478095238 = 5.611213586 Simplifying u + 1.478095238 = 5.611213586 Reorder the terms: 1.478095238 + u = 5.611213586 Solving 1.478095238 + u = 5.611213586 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.478095238' to each side of the equation. 1.478095238 + -1.478095238 + u = 5.611213586 + -1.478095238 Combine like terms: 1.478095238 + -1.478095238 = 0.000000000 0.000000000 + u = 5.611213586 + -1.478095238 u = 5.611213586 + -1.478095238 Combine like terms: 5.611213586 + -1.478095238 = 4.133118348 u = 4.133118348 Simplifying u = 4.133118348Subproblem 2
u + 1.478095238 = -5.611213586 Simplifying u + 1.478095238 = -5.611213586 Reorder the terms: 1.478095238 + u = -5.611213586 Solving 1.478095238 + u = -5.611213586 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.478095238' to each side of the equation. 1.478095238 + -1.478095238 + u = -5.611213586 + -1.478095238 Combine like terms: 1.478095238 + -1.478095238 = 0.000000000 0.000000000 + u = -5.611213586 + -1.478095238 u = -5.611213586 + -1.478095238 Combine like terms: -5.611213586 + -1.478095238 = -7.089308824 u = -7.089308824 Simplifying u = -7.089308824Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.133118348, -7.089308824}
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