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Simplifying 4u4 + -16u3 + 48u2 = 0 Reorder the terms: 48u2 + -16u3 + 4u4 = 0 Solving 48u2 + -16u3 + 4u4 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '4u2'. 4u2(12 + -4u + u2) = 0 Ignore the factor 4.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 '(12 + -4u + u2)' equal to zero and attempt to solve: Simplifying 12 + -4u + u2 = 0 Solving 12 + -4u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -4u + -12 + u2 = 0 + -12 Reorder the terms: 12 + -12 + -4u + u2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -4u + u2 = 0 + -12 -4u + u2 = 0 + -12 Combine like terms: 0 + -12 = -12 -4u + u2 = -12 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 = -12 + 4 Reorder the terms: 4 + -4u + u2 = -12 + 4 Combine like terms: -12 + 4 = -8 4 + -4u + u2 = -8 Factor a perfect square on the left side: (u + -2)(u + -2) = -8 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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