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Simplifying 80a4 + -120a2 + 45 = 0 Reorder the terms: 45 + -120a2 + 80a4 = 0 Solving 45 + -120a2 + 80a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(9 + -24a2 + 16a4) = 0 Factor a trinomial. 5((3 + -4a2)(3 + -4a2)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + -4a2)' equal to zero and attempt to solve: Simplifying 3 + -4a2 = 0 Solving 3 + -4a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4a2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4a2 = 0 + -3 -4a2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4a2 = -3 Divide each side by '-4'. a2 = 0.75 Simplifying a2 = 0.75 Take the square root of each side: a = {-0.866025404, 0.866025404}Subproblem 2
Set the factor '(3 + -4a2)' equal to zero and attempt to solve: Simplifying 3 + -4a2 = 0 Solving 3 + -4a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4a2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4a2 = 0 + -3 -4a2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4a2 = -3 Divide each side by '-4'. a2 = 0.75 Simplifying a2 = 0.75 Take the square root of each side: a = {-0.866025404, 0.866025404}Solution
a = {-0.866025404, 0.866025404, -0.866025404, 0.866025404}
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