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Simplifying u2v + uv + v = 0 Reorder the terms: uv + u2v + v = 0 Solving uv + u2v + v = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), 'v'. v(u + u2 + 1) = 0Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing u to the left, all other terms to the right. Add '-1v' to each side of the equation. v + -1v = 0 + -1v Remove the zero: 0 = -1v Simplifying 0 = -1v The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(u + u2 + 1)' equal to zero and attempt to solve: Simplifying u + u2 + 1 = 0 Reorder the terms: 1 + u + u2 = 0 Solving 1 + u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + u + -1 + u2 = 0 + -1 Reorder the terms: 1 + -1 + u + u2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + u + u2 = 0 + -1 u + u2 = 0 + -1 Combine like terms: 0 + -1 = -1 u + u2 = -1 The u term is u. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. u + 0.25 + u2 = -1 + 0.25 Reorder the terms: 0.25 + u + u2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + u + u2 = -0.75 Factor a perfect square on the left side: (u + 0.5)(u + 0.5) = -0.75 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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