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Simplifying 2u2 + -3u + 11 + -1u2 + -6u + 6 = 0 Reorder the terms: 11 + 6 + -3u + -6u + 2u2 + -1u2 = 0 Combine like terms: 11 + 6 = 17 17 + -3u + -6u + 2u2 + -1u2 = 0 Combine like terms: -3u + -6u = -9u 17 + -9u + 2u2 + -1u2 = 0 Combine like terms: 2u2 + -1u2 = 1u2 17 + -9u + 1u2 = 0 Solving 17 + -9u + 1u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -9u + -17 + u2 = 0 + -17 Reorder the terms: 17 + -17 + -9u + u2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -9u + u2 = 0 + -17 -9u + u2 = 0 + -17 Combine like terms: 0 + -17 = -17 -9u + u2 = -17 The u term is -9u. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9u + 20.25 + u2 = -17 + 20.25 Reorder the terms: 20.25 + -9u + u2 = -17 + 20.25 Combine like terms: -17 + 20.25 = 3.25 20.25 + -9u + u2 = 3.25 Factor a perfect square on the left side: (u + -4.5)(u + -4.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (u + -4.5) equal to 1.802775638 and -1.802775638.Subproblem 1
u + -4.5 = 1.802775638 Simplifying u + -4.5 = 1.802775638 Reorder the terms: -4.5 + u = 1.802775638 Solving -4.5 + u = 1.802775638 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + u = 1.802775638 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = 1.802775638 + 4.5 u = 1.802775638 + 4.5 Combine like terms: 1.802775638 + 4.5 = 6.302775638 u = 6.302775638 Simplifying u = 6.302775638Subproblem 2
u + -4.5 = -1.802775638 Simplifying u + -4.5 = -1.802775638 Reorder the terms: -4.5 + u = -1.802775638 Solving -4.5 + u = -1.802775638 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + u = -1.802775638 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = -1.802775638 + 4.5 u = -1.802775638 + 4.5 Combine like terms: -1.802775638 + 4.5 = 2.697224362 u = 2.697224362 Simplifying u = 2.697224362Solution
The solution to the problem is based on the solutions from the subproblems. u = {6.302775638, 2.697224362}
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