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Simplifying 2u2 + -5u + -16 + -1u2 + -4u + -4 = 0 Reorder the terms: -16 + -4 + -5u + -4u + 2u2 + -1u2 = 0 Combine like terms: -16 + -4 = -20 -20 + -5u + -4u + 2u2 + -1u2 = 0 Combine like terms: -5u + -4u = -9u -20 + -9u + 2u2 + -1u2 = 0 Combine like terms: 2u2 + -1u2 = 1u2 -20 + -9u + 1u2 = 0 Solving -20 + -9u + 1u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -9u + 20 + u2 = 0 + 20 Reorder the terms: -20 + 20 + -9u + u2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -9u + u2 = 0 + 20 -9u + u2 = 0 + 20 Combine like terms: 0 + 20 = 20 -9u + u2 = 20 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 = 20 + 20.25 Reorder the terms: 20.25 + -9u + u2 = 20 + 20.25 Combine like terms: 20 + 20.25 = 40.25 20.25 + -9u + u2 = 40.25 Factor a perfect square on the left side: (u + -4.5)(u + -4.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (u + -4.5) equal to 6.34428877 and -6.34428877.Subproblem 1
u + -4.5 = 6.34428877 Simplifying u + -4.5 = 6.34428877 Reorder the terms: -4.5 + u = 6.34428877 Solving -4.5 + u = 6.34428877 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 = 6.34428877 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = 6.34428877 + 4.5 u = 6.34428877 + 4.5 Combine like terms: 6.34428877 + 4.5 = 10.84428877 u = 10.84428877 Simplifying u = 10.84428877Subproblem 2
u + -4.5 = -6.34428877 Simplifying u + -4.5 = -6.34428877 Reorder the terms: -4.5 + u = -6.34428877 Solving -4.5 + u = -6.34428877 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 = -6.34428877 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = -6.34428877 + 4.5 u = -6.34428877 + 4.5 Combine like terms: -6.34428877 + 4.5 = -1.84428877 u = -1.84428877 Simplifying u = -1.84428877Solution
The solution to the problem is based on the solutions from the subproblems. u = {10.84428877, -1.84428877}
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