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Simplifying 18d5 + 6d4 + 9d3 = 0 Reorder the terms: 9d3 + 6d4 + 18d5 = 0 Solving 9d3 + 6d4 + 18d5 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '3d3'. 3d3(3 + 2d + 6d2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'd3' equal to zero and attempt to solve: Simplifying d3 = 0 Solving d3 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d3 = 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 + 6d2)' equal to zero and attempt to solve: Simplifying 3 + 2d + 6d2 = 0 Solving 3 + 2d + 6d2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.5 + 0.3333333333d + d2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 0.3333333333d + -0.5 + d2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 0.3333333333d + d2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 0.3333333333d + d2 = 0 + -0.5 0.3333333333d + d2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 0.3333333333d + d2 = -0.5 The d term is 0.3333333333d. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333d + 0.02777777779 + d2 = -0.5 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333d + d2 = -0.5 + 0.02777777779 Combine like terms: -0.5 + 0.02777777779 = -0.47222222221 0.02777777779 + 0.3333333333d + d2 = -0.47222222221 Factor a perfect square on the left side: (d + 0.1666666667)(d + 0.1666666667) = -0.47222222221 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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