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Simplifying 42ab + 27a2b2 + 8 = 0 Reorder the terms: 8 + 42ab + 27a2b2 = 0 Solving 8 + 42ab + 27a2b2 = 0 Solving for variable 'a'. Factor a trinomial. (4 + 3ab)(2 + 9ab) = 0Subproblem 1
Set the factor '(4 + 3ab)' equal to zero and attempt to solve: Simplifying 4 + 3ab = 0 Solving 4 + 3ab = 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 + 3ab = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3ab = 0 + -4 3ab = 0 + -4 Combine like terms: 0 + -4 = -4 3ab = -4 Divide each side by '3b'. a = -1.333333333b-1 Simplifying a = -1.333333333b-1Subproblem 2
Set the factor '(2 + 9ab)' equal to zero and attempt to solve: Simplifying 2 + 9ab = 0 Solving 2 + 9ab = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 9ab = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9ab = 0 + -2 9ab = 0 + -2 Combine like terms: 0 + -2 = -2 9ab = -2 Divide each side by '9b'. a = -0.2222222222b-1 Simplifying a = -0.2222222222b-1Solution
a = {-1.333333333b-1, -0.2222222222b-1}
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