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Simplifying 33u2 + -33u + 1 = 0 Reorder the terms: 1 + -33u + 33u2 = 0 Solving 1 + -33u + 33u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 33 the coefficient of the squared term: Divide each side by '33'. 0.0303030303 + -1u + u2 = 0 Move the constant term to the right: Add '-0.0303030303' to each side of the equation. 0.0303030303 + -1u + -0.0303030303 + u2 = 0 + -0.0303030303 Reorder the terms: 0.0303030303 + -0.0303030303 + -1u + u2 = 0 + -0.0303030303 Combine like terms: 0.0303030303 + -0.0303030303 = 0.0000000000 0.0000000000 + -1u + u2 = 0 + -0.0303030303 -1u + u2 = 0 + -0.0303030303 Combine like terms: 0 + -0.0303030303 = -0.0303030303 -1u + u2 = -0.0303030303 The u term is -1u. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1u + 0.25 + u2 = -0.0303030303 + 0.25 Reorder the terms: 0.25 + -1u + u2 = -0.0303030303 + 0.25 Combine like terms: -0.0303030303 + 0.25 = 0.2196969697 0.25 + -1u + u2 = 0.2196969697 Factor a perfect square on the left side: (u + -0.5)(u + -0.5) = 0.2196969697 Calculate the square root of the right side: 0.468718433 Break this problem into two subproblems by setting (u + -0.5) equal to 0.468718433 and -0.468718433.Subproblem 1
u + -0.5 = 0.468718433 Simplifying u + -0.5 = 0.468718433 Reorder the terms: -0.5 + u = 0.468718433 Solving -0.5 + u = 0.468718433 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + u = 0.468718433 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + u = 0.468718433 + 0.5 u = 0.468718433 + 0.5 Combine like terms: 0.468718433 + 0.5 = 0.968718433 u = 0.968718433 Simplifying u = 0.968718433Subproblem 2
u + -0.5 = -0.468718433 Simplifying u + -0.5 = -0.468718433 Reorder the terms: -0.5 + u = -0.468718433 Solving -0.5 + u = -0.468718433 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + u = -0.468718433 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + u = -0.468718433 + 0.5 u = -0.468718433 + 0.5 Combine like terms: -0.468718433 + 0.5 = 0.031281567 u = 0.031281567 Simplifying u = 0.031281567Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.968718433, 0.031281567}
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