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Simplifying 3u4 + 18u3 + 57u2 = 0 Reorder the terms: 57u2 + 18u3 + 3u4 = 0 Solving 57u2 + 18u3 + 3u4 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '3u2'. 3u2(19 + 6u + 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 '(19 + 6u + u2)' equal to zero and attempt to solve: Simplifying 19 + 6u + u2 = 0 Solving 19 + 6u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 6u + -19 + u2 = 0 + -19 Reorder the terms: 19 + -19 + 6u + u2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 6u + u2 = 0 + -19 6u + u2 = 0 + -19 Combine like terms: 0 + -19 = -19 6u + u2 = -19 The u term is 6u. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6u + 9 + u2 = -19 + 9 Reorder the terms: 9 + 6u + u2 = -19 + 9 Combine like terms: -19 + 9 = -10 9 + 6u + u2 = -10 Factor a perfect square on the left side: (u + 3)(u + 3) = -10 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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