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Simplifying 3u6 + 12u5 + 27u4 = 0 Reorder the terms: 27u4 + 12u5 + 3u6 = 0 Solving 27u4 + 12u5 + 3u6 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '3u4'. 3u4(9 + 4u + u2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'u4' equal to zero and attempt to solve: Simplifying u4 = 0 Solving u4 = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u4 = 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 '(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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