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Simplifying (D4 + 4D2 + -2) * Y = 0 Reorder the terms: (-2 + 4D2 + D4) * Y = 0 Reorder the terms for easier multiplication: Y(-2 + 4D2 + D4) = 0 (-2 * Y + 4D2 * Y + D4 * Y) = 0 Reorder the terms: (4D2Y + D4Y + -2Y) = 0 (4D2Y + D4Y + -2Y) = 0 Solving 4D2Y + D4Y + -2Y = 0 Solving for variable 'D'. Factor out the Greatest Common Factor (GCF), 'Y'. Y(4D2 + D4 + -2) = 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 '(4D2 + D4 + -2)' equal to zero and attempt to solve: Simplifying 4D2 + D4 + -2 = 0 Reorder the terms: -2 + 4D2 + D4 = 0 Solving -2 + 4D2 + D4 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 4D2 + 2 + D4 = 0 + 2 Reorder the terms: -2 + 2 + 4D2 + D4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4D2 + D4 = 0 + 2 4D2 + D4 = 0 + 2 Combine like terms: 0 + 2 = 2 4D2 + D4 = 2 The D term is 4D2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4D2 + 4 + D4 = 2 + 4 Reorder the terms: 4 + 4D2 + D4 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + 4D2 + D4 = 6 Factor a perfect square on the left side: (D2 + 2)(D2 + 2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (D2 + 2) equal to 2.449489743 and -2.449489743.Subproblem 1
D2 + 2 = 2.449489743 Simplifying D2 + 2 = 2.449489743 Reorder the terms: 2 + D2 = 2.449489743 Solving 2 + D2 = 2.449489743 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + D2 = 2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + D2 = 2.449489743 + -2 D2 = 2.449489743 + -2 Combine like terms: 2.449489743 + -2 = 0.449489743 D2 = 0.449489743 Simplifying D2 = 0.449489743 Take the square root of each side: D = {-0.670439962, 0.670439962}Subproblem 2
D2 + 2 = -2.449489743 Simplifying D2 + 2 = -2.449489743 Reorder the terms: 2 + D2 = -2.449489743 Solving 2 + D2 = -2.449489743 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + D2 = -2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + D2 = -2.449489743 + -2 D2 = -2.449489743 + -2 Combine like terms: -2.449489743 + -2 = -4.449489743 D2 = -4.449489743 Simplifying D2 = -4.449489743 Reorder the terms: 4.449489743 + D2 = -4.449489743 + 4.449489743 Combine like terms: -4.449489743 + 4.449489743 = 0.000000000 4.449489743 + D2 = 0.000000000 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. 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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