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Simplifying 3u7 + 21u6 + 45u5 = 0 Reorder the terms: 45u5 + 21u6 + 3u7 = 0 Solving 45u5 + 21u6 + 3u7 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '3u5'. 3u5(15 + 7u + u2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'u5' equal to zero and attempt to solve: Simplifying u5 = 0 Solving u5 = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u5 = 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 '(15 + 7u + u2)' equal to zero and attempt to solve: Simplifying 15 + 7u + u2 = 0 Solving 15 + 7u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 7u + -15 + u2 = 0 + -15 Reorder the terms: 15 + -15 + 7u + u2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 7u + u2 = 0 + -15 7u + u2 = 0 + -15 Combine like terms: 0 + -15 = -15 7u + u2 = -15 The u term is 7u. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7u + 12.25 + u2 = -15 + 12.25 Reorder the terms: 12.25 + 7u + u2 = -15 + 12.25 Combine like terms: -15 + 12.25 = -2.75 12.25 + 7u + u2 = -2.75 Factor a perfect square on the left side: (u + 3.5)(u + 3.5) = -2.75 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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