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Simplifying 54a4 + -36a2 + 6 = 0 Reorder the terms: 6 + -36a2 + 54a4 = 0 Solving 6 + -36a2 + 54a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6'. 6(1 + -6a2 + 9a4) = 0 Factor a trinomial. 6((1 + -3a2)(1 + -3a2)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(1 + -3a2)' equal to zero and attempt to solve: Simplifying 1 + -3a2 = 0 Solving 1 + -3a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3a2 = 0 + -1 -3a2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3a2 = -1 Divide each side by '-3'. a2 = 0.3333333333 Simplifying a2 = 0.3333333333 Take the square root of each side: a = {-0.577350269, 0.577350269}Subproblem 2
Set the factor '(1 + -3a2)' equal to zero and attempt to solve: Simplifying 1 + -3a2 = 0 Solving 1 + -3a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3a2 = 0 + -1 -3a2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3a2 = -1 Divide each side by '-3'. a2 = 0.3333333333 Simplifying a2 = 0.3333333333 Take the square root of each side: a = {-0.577350269, 0.577350269}Solution
a = {-0.577350269, 0.577350269, -0.577350269, 0.577350269}
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