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Simplifying 5u4 + -30u3 + 70u2 = 0 Reorder the terms: 70u2 + -30u3 + 5u4 = 0 Solving 70u2 + -30u3 + 5u4 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '5u2'. 5u2(14 + -6u + u2) = 0 Ignore the factor 5.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 '(14 + -6u + u2)' equal to zero and attempt to solve: Simplifying 14 + -6u + u2 = 0 Solving 14 + -6u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -6u + -14 + u2 = 0 + -14 Reorder the terms: 14 + -14 + -6u + u2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -6u + u2 = 0 + -14 -6u + u2 = 0 + -14 Combine like terms: 0 + -14 = -14 -6u + u2 = -14 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 = -14 + 9 Reorder the terms: 9 + -6u + u2 = -14 + 9 Combine like terms: -14 + 9 = -5 9 + -6u + u2 = -5 Factor a perfect square on the left side: (u + -3)(u + -3) = -5 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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