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Simplifying 6d4u + 12d3u + 18d2u = 0 Reorder the terms: 18d2u + 12d3u + 6d4u = 0 Solving 18d2u + 12d3u + 6d4u = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '6d2u'. 6d2u(3 + 2d + d2) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'd2u' equal to zero and attempt to solve: Simplifying d2u = 0 Solving d2u = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d2u = 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 '(3 + 2d + d2)' equal to zero and attempt to solve: Simplifying 3 + 2d + d2 = 0 Solving 3 + 2d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 2d + -3 + d2 = 0 + -3 Reorder the terms: 3 + -3 + 2d + d2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2d + d2 = 0 + -3 2d + d2 = 0 + -3 Combine like terms: 0 + -3 = -3 2d + d2 = -3 The d term is 2d. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2d + 1 + d2 = -3 + 1 Reorder the terms: 1 + 2d + d2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + 2d + d2 = -2 Factor a perfect square on the left side: (d + 1)(d + 1) = -2 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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