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Simplifying u4 + 8u3 + 20u2 = 0 Reorder the terms: 20u2 + 8u3 + u4 = 0 Solving 20u2 + 8u3 + u4 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), 'u2'. u2(20 + 8u + u2) = 0Subproblem 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 '(20 + 8u + u2)' equal to zero and attempt to solve: Simplifying 20 + 8u + u2 = 0 Solving 20 + 8u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 8u + -20 + u2 = 0 + -20 Reorder the terms: 20 + -20 + 8u + u2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 8u + u2 = 0 + -20 8u + u2 = 0 + -20 Combine like terms: 0 + -20 = -20 8u + u2 = -20 The u term is 8u. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8u + 16 + u2 = -20 + 16 Reorder the terms: 16 + 8u + u2 = -20 + 16 Combine like terms: -20 + 16 = -4 16 + 8u + u2 = -4 Factor a perfect square on the left side: (u + 4)(u + 4) = -4 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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