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Simplifying -9u + -5 = u2 + -5u + 4 Reorder the terms: -5 + -9u = u2 + -5u + 4 Reorder the terms: -5 + -9u = 4 + -5u + u2 Solving -5 + -9u = 4 + -5u + u2 Solving for variable 'u'. Reorder the terms: -5 + -4 + -9u + 5u + -1u2 = 4 + -5u + u2 + -4 + 5u + -1u2 Combine like terms: -5 + -4 = -9 -9 + -9u + 5u + -1u2 = 4 + -5u + u2 + -4 + 5u + -1u2 Combine like terms: -9u + 5u = -4u -9 + -4u + -1u2 = 4 + -5u + u2 + -4 + 5u + -1u2 Reorder the terms: -9 + -4u + -1u2 = 4 + -4 + -5u + 5u + u2 + -1u2 Combine like terms: 4 + -4 = 0 -9 + -4u + -1u2 = 0 + -5u + 5u + u2 + -1u2 -9 + -4u + -1u2 = -5u + 5u + u2 + -1u2 Combine like terms: -5u + 5u = 0 -9 + -4u + -1u2 = 0 + u2 + -1u2 -9 + -4u + -1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 -9 + -4u + -1u2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 4u + u2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 4u + u2)' equal to zero and attempt to solve: Simplifying 9 + 4u + u2 = 0 Solving 9 + 4u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 4u + -9 + u2 = 0 + -9 Reorder the terms: 9 + -9 + 4u + u2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4u + u2 = 0 + -9 4u + u2 = 0 + -9 Combine like terms: 0 + -9 = -9 4u + u2 = -9 The u term is 4u. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4u + 4 + u2 = -9 + 4 Reorder the terms: 4 + 4u + u2 = -9 + 4 Combine like terms: -9 + 4 = -5 4 + 4u + u2 = -5 Factor a perfect square on the left side: (u + 2)(u + 2) = -5 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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