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Simplifying 16d3 + 24d2 + 32d = 0 Reorder the terms: 32d + 24d2 + 16d3 = 0 Solving 32d + 24d2 + 16d3 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '8d'. 8d(4 + 3d + 2d2) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(4 + 3d + 2d2)' equal to zero and attempt to solve: Simplifying 4 + 3d + 2d2 = 0 Solving 4 + 3d + 2d2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + 1.5d + d2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 1.5d + -2 + d2 = 0 + -2 Reorder the terms: 2 + -2 + 1.5d + d2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 1.5d + d2 = 0 + -2 1.5d + d2 = 0 + -2 Combine like terms: 0 + -2 = -2 1.5d + d2 = -2 The d term is 1.5d. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5d + 0.5625 + d2 = -2 + 0.5625 Reorder the terms: 0.5625 + 1.5d + d2 = -2 + 0.5625 Combine like terms: -2 + 0.5625 = -1.4375 0.5625 + 1.5d + d2 = -1.4375 Factor a perfect square on the left side: (d + 0.75)(d + 0.75) = -1.4375 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.Solution
d = {0}
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