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Simplifying 54a4 + -288a2 + 384 = 0 Reorder the terms: 384 + -288a2 + 54a4 = 0 Solving 384 + -288a2 + 54a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6'. 6(64 + -48a2 + 9a4) = 0 Factor a trinomial. 6((8 + -3a2)(8 + -3a2)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(8 + -3a2)' equal to zero and attempt to solve: Simplifying 8 + -3a2 = 0 Solving 8 + -3a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3a2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3a2 = 0 + -8 -3a2 = 0 + -8 Combine like terms: 0 + -8 = -8 -3a2 = -8 Divide each side by '-3'. a2 = 2.666666667 Simplifying a2 = 2.666666667 Take the square root of each side: a = {-1.632993162, 1.632993162}Subproblem 2
Set the factor '(8 + -3a2)' equal to zero and attempt to solve: Simplifying 8 + -3a2 = 0 Solving 8 + -3a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3a2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3a2 = 0 + -8 -3a2 = 0 + -8 Combine like terms: 0 + -8 = -8 -3a2 = -8 Divide each side by '-3'. a2 = 2.666666667 Simplifying a2 = 2.666666667 Take the square root of each side: a = {-1.632993162, 1.632993162}Solution
a = {-1.632993162, 1.632993162, -1.632993162, 1.632993162}
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