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Simplifying 5u5 + 20u4 + 50u3 = 0 Reorder the terms: 50u3 + 20u4 + 5u5 = 0 Solving 50u3 + 20u4 + 5u5 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '5u3'. 5u3(10 + 4u + u2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'u3' equal to zero and attempt to solve: Simplifying u3 = 0 Solving u3 = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u3 = 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 '(10 + 4u + u2)' equal to zero and attempt to solve: Simplifying 10 + 4u + u2 = 0 Solving 10 + 4u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 4u + -10 + u2 = 0 + -10 Reorder the terms: 10 + -10 + 4u + u2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 4u + u2 = 0 + -10 4u + u2 = 0 + -10 Combine like terms: 0 + -10 = -10 4u + u2 = -10 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 = -10 + 4 Reorder the terms: 4 + 4u + u2 = -10 + 4 Combine like terms: -10 + 4 = -6 4 + 4u + u2 = -6 Factor a perfect square on the left side: (u + 2)(u + 2) = -6 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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