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Simplifying 6u3 + 24u2 + 6u = 0 Reorder the terms: 6u + 24u2 + 6u3 = 0 Solving 6u + 24u2 + 6u3 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '6u'. 6u(1 + 4u + u2) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'u' equal to zero and attempt to solve: Simplifying u = 0 Solving u = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u = 0Subproblem 2
Set the factor '(1 + 4u + u2)' equal to zero and attempt to solve: Simplifying 1 + 4u + u2 = 0 Solving 1 + 4u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4u + -1 + u2 = 0 + -1 Reorder the terms: 1 + -1 + 4u + u2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4u + u2 = 0 + -1 4u + u2 = 0 + -1 Combine like terms: 0 + -1 = -1 4u + u2 = -1 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 = -1 + 4 Reorder the terms: 4 + 4u + u2 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + 4u + u2 = 3 Factor a perfect square on the left side: (u + 2)(u + 2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (u + 2) equal to 1.732050808 and -1.732050808.Subproblem 1
u + 2 = 1.732050808 Simplifying u + 2 = 1.732050808 Reorder the terms: 2 + u = 1.732050808 Solving 2 + u = 1.732050808 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + u = 1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + u = 1.732050808 + -2 u = 1.732050808 + -2 Combine like terms: 1.732050808 + -2 = -0.267949192 u = -0.267949192 Simplifying u = -0.267949192Subproblem 2
u + 2 = -1.732050808 Simplifying u + 2 = -1.732050808 Reorder the terms: 2 + u = -1.732050808 Solving 2 + u = -1.732050808 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + u = -1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + u = -1.732050808 + -2 u = -1.732050808 + -2 Combine like terms: -1.732050808 + -2 = -3.732050808 u = -3.732050808 Simplifying u = -3.732050808Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.267949192, -3.732050808}Solution
u = {0, -0.267949192, -3.732050808}
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