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Simplifying -7u4(4u2 + 9u + -6) = 0 Reorder the terms: -7u4(-6 + 9u + 4u2) = 0 (-6 * -7u4 + 9u * -7u4 + 4u2 * -7u4) = 0 (42u4 + -63u5 + -28u6) = 0 Solving 42u4 + -63u5 + -28u6 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '7u4'. 7u4(6 + -9u + -4u2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'u4' equal to zero and attempt to solve: Simplifying u4 = 0 Solving u4 = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u4 = 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 '(6 + -9u + -4u2)' equal to zero and attempt to solve: Simplifying 6 + -9u + -4u2 = 0 Solving 6 + -9u + -4u2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.5 + 2.25u + u2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 2.25u + 1.5 + u2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 2.25u + u2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 2.25u + u2 = 0 + 1.5 2.25u + u2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 2.25u + u2 = 1.5 The u term is 2.25u. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25u + 1.265625 + u2 = 1.5 + 1.265625 Reorder the terms: 1.265625 + 2.25u + u2 = 1.5 + 1.265625 Combine like terms: 1.5 + 1.265625 = 2.765625 1.265625 + 2.25u + u2 = 2.765625 Factor a perfect square on the left side: (u + 1.125)(u + 1.125) = 2.765625 Calculate the square root of the right side: 1.663016837 Break this problem into two subproblems by setting (u + 1.125) equal to 1.663016837 and -1.663016837.Subproblem 1
u + 1.125 = 1.663016837 Simplifying u + 1.125 = 1.663016837 Reorder the terms: 1.125 + u = 1.663016837 Solving 1.125 + u = 1.663016837 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + u = 1.663016837 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + u = 1.663016837 + -1.125 u = 1.663016837 + -1.125 Combine like terms: 1.663016837 + -1.125 = 0.538016837 u = 0.538016837 Simplifying u = 0.538016837Subproblem 2
u + 1.125 = -1.663016837 Simplifying u + 1.125 = -1.663016837 Reorder the terms: 1.125 + u = -1.663016837 Solving 1.125 + u = -1.663016837 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + u = -1.663016837 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + u = -1.663016837 + -1.125 u = -1.663016837 + -1.125 Combine like terms: -1.663016837 + -1.125 = -2.788016837 u = -2.788016837 Simplifying u = -2.788016837Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.538016837, -2.788016837}Solution
u = {0.538016837, -2.788016837}
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