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Simplifying 3u4 + -9u3 + 27u2 = 0 Reorder the terms: 27u2 + -9u3 + 3u4 = 0 Solving 27u2 + -9u3 + 3u4 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '3u2'. 3u2(9 + -3u + u2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'u2' equal to zero and attempt to solve: Simplifying u2 = 0 Solving u2 = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u2 = 0 Take the square root of each side: u = {0}Subproblem 2
Set the factor '(9 + -3u + u2)' equal to zero and attempt to solve: Simplifying 9 + -3u + u2 = 0 Solving 9 + -3u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -3u + -9 + u2 = 0 + -9 Reorder the terms: 9 + -9 + -3u + u2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -3u + u2 = 0 + -9 -3u + u2 = 0 + -9 Combine like terms: 0 + -9 = -9 -3u + u2 = -9 The u term is -3u. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3u + 2.25 + u2 = -9 + 2.25 Reorder the terms: 2.25 + -3u + u2 = -9 + 2.25 Combine like terms: -9 + 2.25 = -6.75 2.25 + -3u + u2 = -6.75 Factor a perfect square on the left side: (u + -1.5)(u + -1.5) = -6.75 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.Solution
u = {0}
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