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Simplifying 54a2 + 39ab + -8b2 = 0 Reorder the terms: 39ab + 54a2 + -8b2 = 0 Solving 39ab + 54a2 + -8b2 = 0 Solving for variable 'a'. Factor a trinomial. (6a + -1b)(9a + 8b) = 0Subproblem 1
Set the factor '(6a + -1b)' equal to zero and attempt to solve: Simplifying 6a + -1b = 0 Solving 6a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 6a + -1b + b = 0 + b Combine like terms: -1b + b = 0 6a + 0 = 0 + b 6a = 0 + b Remove the zero: 6a = b Divide each side by '6'. a = 0.1666666667b Simplifying a = 0.1666666667bSubproblem 2
Set the factor '(9a + 8b)' equal to zero and attempt to solve: Simplifying 9a + 8b = 0 Solving 9a + 8b = 0 Move all terms containing a to the left, all other terms to the right. Add '-8b' to each side of the equation. 9a + 8b + -8b = 0 + -8b Combine like terms: 8b + -8b = 0 9a + 0 = 0 + -8b 9a = 0 + -8b Remove the zero: 9a = -8b Divide each side by '9'. a = -0.8888888889b Simplifying a = -0.8888888889bSolution
a = {0.1666666667b, -0.8888888889b}
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