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Simplifying u2 + 1 = 2u2 + 5u + 11 Reorder the terms: 1 + u2 = 2u2 + 5u + 11 Reorder the terms: 1 + u2 = 11 + 5u + 2u2 Solving 1 + u2 = 11 + 5u + 2u2 Solving for variable 'u'. Reorder the terms: 1 + -11 + -5u + u2 + -2u2 = 11 + 5u + 2u2 + -11 + -5u + -2u2 Combine like terms: 1 + -11 = -10 -10 + -5u + u2 + -2u2 = 11 + 5u + 2u2 + -11 + -5u + -2u2 Combine like terms: u2 + -2u2 = -1u2 -10 + -5u + -1u2 = 11 + 5u + 2u2 + -11 + -5u + -2u2 Reorder the terms: -10 + -5u + -1u2 = 11 + -11 + 5u + -5u + 2u2 + -2u2 Combine like terms: 11 + -11 = 0 -10 + -5u + -1u2 = 0 + 5u + -5u + 2u2 + -2u2 -10 + -5u + -1u2 = 5u + -5u + 2u2 + -2u2 Combine like terms: 5u + -5u = 0 -10 + -5u + -1u2 = 0 + 2u2 + -2u2 -10 + -5u + -1u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 -10 + -5u + -1u2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 5u + u2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 5u + u2)' equal to zero and attempt to solve: Simplifying 10 + 5u + u2 = 0 Solving 10 + 5u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 5u + -10 + u2 = 0 + -10 Reorder the terms: 10 + -10 + 5u + u2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 5u + u2 = 0 + -10 5u + u2 = 0 + -10 Combine like terms: 0 + -10 = -10 5u + u2 = -10 The u term is 5u. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5u + 6.25 + u2 = -10 + 6.25 Reorder the terms: 6.25 + 5u + u2 = -10 + 6.25 Combine like terms: -10 + 6.25 = -3.75 6.25 + 5u + u2 = -3.75 Factor a perfect square on the left side: (u + 2.5)(u + 2.5) = -3.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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