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Simplifying 2u2 + -9u + 11 = u2 + -1 Reorder the terms: 11 + -9u + 2u2 = u2 + -1 Reorder the terms: 11 + -9u + 2u2 = -1 + u2 Solving 11 + -9u + 2u2 = -1 + u2 Solving for variable 'u'. Reorder the terms: 11 + 1 + -9u + 2u2 + -1u2 = -1 + u2 + 1 + -1u2 Combine like terms: 11 + 1 = 12 12 + -9u + 2u2 + -1u2 = -1 + u2 + 1 + -1u2 Combine like terms: 2u2 + -1u2 = 1u2 12 + -9u + 1u2 = -1 + u2 + 1 + -1u2 Reorder the terms: 12 + -9u + 1u2 = -1 + 1 + u2 + -1u2 Combine like terms: -1 + 1 = 0 12 + -9u + 1u2 = 0 + u2 + -1u2 12 + -9u + 1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 12 + -9u + 1u2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -9u + -12 + u2 = 0 + -12 Reorder the terms: 12 + -12 + -9u + u2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -9u + u2 = 0 + -12 -9u + u2 = 0 + -12 Combine like terms: 0 + -12 = -12 -9u + u2 = -12 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 = -12 + 20.25 Reorder the terms: 20.25 + -9u + u2 = -12 + 20.25 Combine like terms: -12 + 20.25 = 8.25 20.25 + -9u + u2 = 8.25 Factor a perfect square on the left side: (u + -4.5)(u + -4.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (u + -4.5) equal to 2.872281323 and -2.872281323.Subproblem 1
u + -4.5 = 2.872281323 Simplifying u + -4.5 = 2.872281323 Reorder the terms: -4.5 + u = 2.872281323 Solving -4.5 + u = 2.872281323 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 = 2.872281323 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = 2.872281323 + 4.5 u = 2.872281323 + 4.5 Combine like terms: 2.872281323 + 4.5 = 7.372281323 u = 7.372281323 Simplifying u = 7.372281323Subproblem 2
u + -4.5 = -2.872281323 Simplifying u + -4.5 = -2.872281323 Reorder the terms: -4.5 + u = -2.872281323 Solving -4.5 + u = -2.872281323 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 = -2.872281323 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = -2.872281323 + 4.5 u = -2.872281323 + 4.5 Combine like terms: -2.872281323 + 4.5 = 1.627718677 u = 1.627718677 Simplifying u = 1.627718677Solution
The solution to the problem is based on the solutions from the subproblems. u = {7.372281323, 1.627718677}
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