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Simplifying u2 + -9u + -35 = 0 Reorder the terms: -35 + -9u + u2 = 0 Solving -35 + -9u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -9u + 35 + u2 = 0 + 35 Reorder the terms: -35 + 35 + -9u + u2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -9u + u2 = 0 + 35 -9u + u2 = 0 + 35 Combine like terms: 0 + 35 = 35 -9u + u2 = 35 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 = 35 + 20.25 Reorder the terms: 20.25 + -9u + u2 = 35 + 20.25 Combine like terms: 35 + 20.25 = 55.25 20.25 + -9u + u2 = 55.25 Factor a perfect square on the left side: (u + -4.5)(u + -4.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (u + -4.5) equal to 7.433034374 and -7.433034374.Subproblem 1
u + -4.5 = 7.433034374 Simplifying u + -4.5 = 7.433034374 Reorder the terms: -4.5 + u = 7.433034374 Solving -4.5 + u = 7.433034374 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 = 7.433034374 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = 7.433034374 + 4.5 u = 7.433034374 + 4.5 Combine like terms: 7.433034374 + 4.5 = 11.933034374 u = 11.933034374 Simplifying u = 11.933034374Subproblem 2
u + -4.5 = -7.433034374 Simplifying u + -4.5 = -7.433034374 Reorder the terms: -4.5 + u = -7.433034374 Solving -4.5 + u = -7.433034374 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 = -7.433034374 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = -7.433034374 + 4.5 u = -7.433034374 + 4.5 Combine like terms: -7.433034374 + 4.5 = -2.933034374 u = -2.933034374 Simplifying u = -2.933034374Solution
The solution to the problem is based on the solutions from the subproblems. u = {11.933034374, -2.933034374}
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