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Simplifying (d4 + 2d3 + 10d2) * y = 0 Reorder the terms: (10d2 + 2d3 + d4) * y = 0 Reorder the terms for easier multiplication: y(10d2 + 2d3 + d4) = 0 (10d2 * y + 2d3 * y + d4 * y) = 0 (10d2y + 2d3y + d4y) = 0 Solving 10d2y + 2d3y + d4y = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), 'd2y'. d2y(10 + 2d + d2) = 0Subproblem 1
Set the factor 'd2y' equal to zero and attempt to solve: Simplifying d2y = 0 Solving d2y = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d2y = 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 '(10 + 2d + d2)' equal to zero and attempt to solve: Simplifying 10 + 2d + d2 = 0 Solving 10 + 2d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 2d + -10 + d2 = 0 + -10 Reorder the terms: 10 + -10 + 2d + d2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 2d + d2 = 0 + -10 2d + d2 = 0 + -10 Combine like terms: 0 + -10 = -10 2d + d2 = -10 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 = -10 + 1 Reorder the terms: 1 + 2d + d2 = -10 + 1 Combine like terms: -10 + 1 = -9 1 + 2d + d2 = -9 Factor a perfect square on the left side: (d + 1)(d + 1) = -9 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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