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Simplifying u5 + 17u4 + 80u3 = 0 Reorder the terms: 80u3 + 17u4 + u5 = 0 Solving 80u3 + 17u4 + u5 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), 'u3'. u3(80 + 17u + u2) = 0Subproblem 1
Set the factor 'u3' equal to zero and attempt to solve: Simplifying u3 = 0 Solving u3 = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u3 = 0 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 '(80 + 17u + u2)' equal to zero and attempt to solve: Simplifying 80 + 17u + u2 = 0 Solving 80 + 17u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + 17u + -80 + u2 = 0 + -80 Reorder the terms: 80 + -80 + 17u + u2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 17u + u2 = 0 + -80 17u + u2 = 0 + -80 Combine like terms: 0 + -80 = -80 17u + u2 = -80 The u term is 17u. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17u + 72.25 + u2 = -80 + 72.25 Reorder the terms: 72.25 + 17u + u2 = -80 + 72.25 Combine like terms: -80 + 72.25 = -7.75 72.25 + 17u + u2 = -7.75 Factor a perfect square on the left side: (u + 8.5)(u + 8.5) = -7.75 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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