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Simplifying (d3 + 4d2 + 5d) * y = 0 Reorder the terms: (5d + 4d2 + d3) * y = 0 Reorder the terms for easier multiplication: y(5d + 4d2 + d3) = 0 (5d * y + 4d2 * y + d3 * y) = 0 (5dy + 4d2y + d3y) = 0 Solving 5dy + 4d2y + d3y = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), 'dy'. dy(5 + 4d + d2) = 0Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(5 + 4d + d2)' equal to zero and attempt to solve: Simplifying 5 + 4d + d2 = 0 Solving 5 + 4d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 4d + -5 + d2 = 0 + -5 Reorder the terms: 5 + -5 + 4d + d2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4d + d2 = 0 + -5 4d + d2 = 0 + -5 Combine like terms: 0 + -5 = -5 4d + d2 = -5 The d term is 4d. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4d + 4 + d2 = -5 + 4 Reorder the terms: 4 + 4d + d2 = -5 + 4 Combine like terms: -5 + 4 = -1 4 + 4d + d2 = -1 Factor a perfect square on the left side: (d + 2)(d + 2) = -1 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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