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Simplifying 2u4 + -30u2 = 112 Reorder the terms: -30u2 + 2u4 = 112 Solving -30u2 + 2u4 = 112 Solving for variable 'u'. Reorder the terms: -112 + -30u2 + 2u4 = 112 + -112 Combine like terms: 112 + -112 = 0 -112 + -30u2 + 2u4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-56 + -15u2 + u4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-56 + -15u2 + u4)' equal to zero and attempt to solve: Simplifying -56 + -15u2 + u4 = 0 Solving -56 + -15u2 + u4 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -15u2 + 56 + u4 = 0 + 56 Reorder the terms: -56 + 56 + -15u2 + u4 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -15u2 + u4 = 0 + 56 -15u2 + u4 = 0 + 56 Combine like terms: 0 + 56 = 56 -15u2 + u4 = 56 The u term is -15u2. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15u2 + 56.25 + u4 = 56 + 56.25 Reorder the terms: 56.25 + -15u2 + u4 = 56 + 56.25 Combine like terms: 56 + 56.25 = 112.25 56.25 + -15u2 + u4 = 112.25 Factor a perfect square on the left side: (u2 + -7.5)(u2 + -7.5) = 112.25 Calculate the square root of the right side: 10.59481005 Break this problem into two subproblems by setting (u2 + -7.5) equal to 10.59481005 and -10.59481005.Subproblem 1
u2 + -7.5 = 10.59481005 Simplifying u2 + -7.5 = 10.59481005 Reorder the terms: -7.5 + u2 = 10.59481005 Solving -7.5 + u2 = 10.59481005 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + u2 = 10.59481005 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + u2 = 10.59481005 + 7.5 u2 = 10.59481005 + 7.5 Combine like terms: 10.59481005 + 7.5 = 18.09481005 u2 = 18.09481005 Simplifying u2 = 18.09481005 Take the square root of each side: u = {-4.253799484, 4.253799484}Subproblem 2
u2 + -7.5 = -10.59481005 Simplifying u2 + -7.5 = -10.59481005 Reorder the terms: -7.5 + u2 = -10.59481005 Solving -7.5 + u2 = -10.59481005 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + u2 = -10.59481005 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + u2 = -10.59481005 + 7.5 u2 = -10.59481005 + 7.5 Combine like terms: -10.59481005 + 7.5 = -3.09481005 u2 = -3.09481005 Simplifying u2 = -3.09481005 Reorder the terms: 3.09481005 + u2 = -3.09481005 + 3.09481005 Combine like terms: -3.09481005 + 3.09481005 = 0.00000000 3.09481005 + u2 = 0.00000000 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. 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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