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Simplifying -6u2 + -3u + 8 = 0 Reorder the terms: 8 + -3u + -6u2 = 0 Solving 8 + -3u + -6u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.333333333 + 0.5u + u2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 0.5u + 1.333333333 + u2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 0.5u + u2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 0.5u + u2 = 0 + 1.333333333 0.5u + u2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 0.5u + u2 = 1.333333333 The u term is 0.5u. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5u + 0.0625 + u2 = 1.333333333 + 0.0625 Reorder the terms: 0.0625 + 0.5u + u2 = 1.333333333 + 0.0625 Combine like terms: 1.333333333 + 0.0625 = 1.395833333 0.0625 + 0.5u + u2 = 1.395833333 Factor a perfect square on the left side: (u + 0.25)(u + 0.25) = 1.395833333 Calculate the square root of the right side: 1.181453906 Break this problem into two subproblems by setting (u + 0.25) equal to 1.181453906 and -1.181453906.Subproblem 1
u + 0.25 = 1.181453906 Simplifying u + 0.25 = 1.181453906 Reorder the terms: 0.25 + u = 1.181453906 Solving 0.25 + u = 1.181453906 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + u = 1.181453906 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + u = 1.181453906 + -0.25 u = 1.181453906 + -0.25 Combine like terms: 1.181453906 + -0.25 = 0.931453906 u = 0.931453906 Simplifying u = 0.931453906Subproblem 2
u + 0.25 = -1.181453906 Simplifying u + 0.25 = -1.181453906 Reorder the terms: 0.25 + u = -1.181453906 Solving 0.25 + u = -1.181453906 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + u = -1.181453906 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + u = -1.181453906 + -0.25 u = -1.181453906 + -0.25 Combine like terms: -1.181453906 + -0.25 = -1.431453906 u = -1.431453906 Simplifying u = -1.431453906Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.931453906, -1.431453906}
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