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Simplifying 45a4 + -120a2 + 80 = 0 Reorder the terms: 80 + -120a2 + 45a4 = 0 Solving 80 + -120a2 + 45a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(16 + -24a2 + 9a4) = 0 Factor a trinomial. 5((4 + -3a2)(4 + -3a2)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + -3a2)' equal to zero and attempt to solve: Simplifying 4 + -3a2 = 0 Solving 4 + -3a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3a2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a2 = 0 + -4 -3a2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3a2 = -4 Divide each side by '-3'. a2 = 1.333333333 Simplifying a2 = 1.333333333 Take the square root of each side: a = {-1.154700538, 1.154700538}Subproblem 2
Set the factor '(4 + -3a2)' equal to zero and attempt to solve: Simplifying 4 + -3a2 = 0 Solving 4 + -3a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3a2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a2 = 0 + -4 -3a2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3a2 = -4 Divide each side by '-3'. a2 = 1.333333333 Simplifying a2 = 1.333333333 Take the square root of each side: a = {-1.154700538, 1.154700538}Solution
a = {-1.154700538, 1.154700538, -1.154700538, 1.154700538}
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