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Simplifying 18a2 + -5b2 + 27ab = 0 Reorder the terms: 27ab + 18a2 + -5b2 = 0 Solving 27ab + 18a2 + -5b2 = 0 Solving for variable 'a'. Factor a trinomial. (6a + -1b)(3a + 5b) = 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 '(3a + 5b)' equal to zero and attempt to solve: Simplifying 3a + 5b = 0 Solving 3a + 5b = 0 Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. 3a + 5b + -5b = 0 + -5b Combine like terms: 5b + -5b = 0 3a + 0 = 0 + -5b 3a = 0 + -5b Remove the zero: 3a = -5b Divide each side by '3'. a = -1.666666667b Simplifying a = -1.666666667bSolution
a = {0.1666666667b, -1.666666667b}
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