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Simplifying D6 + -4D4 + 4D2 = 0 Reorder the terms: 4D2 + -4D4 + D6 = 0 Solving 4D2 + -4D4 + D6 = 0 Solving for variable 'D'. Factor out the Greatest Common Factor (GCF), 'D2'. D2(4 + -4D2 + D4) = 0 Factor a trinomial. D2((2 + -1D2)(2 + -1D2)) = 0Subproblem 1
Set the factor 'D2' equal to zero and attempt to solve: Simplifying D2 = 0 Solving D2 = 0 Move all terms containing D to the left, all other terms to the right. Simplifying D2 = 0 Take the square root of each side: D = {0}Subproblem 2
Set the factor '(2 + -1D2)' equal to zero and attempt to solve: Simplifying 2 + -1D2 = 0 Solving 2 + -1D2 = 0 Move all terms containing D to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1D2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1D2 = 0 + -2 -1D2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1D2 = -2 Divide each side by '-1'. D2 = 2 Simplifying D2 = 2 Take the square root of each side: D = {-1.414213562, 1.414213562}Subproblem 3
Set the factor '(2 + -1D2)' equal to zero and attempt to solve: Simplifying 2 + -1D2 = 0 Solving 2 + -1D2 = 0 Move all terms containing D to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1D2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1D2 = 0 + -2 -1D2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1D2 = -2 Divide each side by '-1'. D2 = 2 Simplifying D2 = 2 Take the square root of each side: D = {-1.414213562, 1.414213562}Solution
D = {0, -1.414213562, 1.414213562, -1.414213562, 1.414213562}
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