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Simplifying 20a4 + -39a2 + 18 = 0 Reorder the terms: 18 + -39a2 + 20a4 = 0 Solving 18 + -39a2 + 20a4 = 0 Solving for variable 'a'. Factor a trinomial. (3 + -4a2)(6 + -5a2) = 0Subproblem 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 '(6 + -5a2)' equal to zero and attempt to solve: Simplifying 6 + -5a2 = 0 Solving 6 + -5a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5a2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5a2 = 0 + -6 -5a2 = 0 + -6 Combine like terms: 0 + -6 = -6 -5a2 = -6 Divide each side by '-5'. a2 = 1.2 Simplifying a2 = 1.2 Take the square root of each side: a = {-1.095445115, 1.095445115}Solution
a = {-0.866025404, 0.866025404, -1.095445115, 1.095445115}
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