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