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Simplifying 54a4 + -180a2 + 150 = 0 Reorder the terms: 150 + -180a2 + 54a4 = 0 Solving 150 + -180a2 + 54a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6'. 6(25 + -30a2 + 9a4) = 0 Factor a trinomial. 6((5 + -3a2)(5 + -3a2)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(5 + -3a2)' equal to zero and attempt to solve: Simplifying 5 + -3a2 = 0 Solving 5 + -3a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3a2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3a2 = 0 + -5 -3a2 = 0 + -5 Combine like terms: 0 + -5 = -5 -3a2 = -5 Divide each side by '-3'. a2 = 1.666666667 Simplifying a2 = 1.666666667 Take the square root of each side: a = {-1.290994449, 1.290994449}Subproblem 2
Set the factor '(5 + -3a2)' equal to zero and attempt to solve: Simplifying 5 + -3a2 = 0 Solving 5 + -3a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3a2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3a2 = 0 + -5 -3a2 = 0 + -5 Combine like terms: 0 + -5 = -5 -3a2 = -5 Divide each side by '-3'. a2 = 1.666666667 Simplifying a2 = 1.666666667 Take the square root of each side: a = {-1.290994449, 1.290994449}Solution
a = {-1.290994449, 1.290994449, -1.290994449, 1.290994449}
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