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Simplifying 18a2 + -27ab + 10b2 = 0 Reorder the terms: -27ab + 18a2 + 10b2 = 0 Solving -27ab + 18a2 + 10b2 = 0 Solving for variable 'a'. Factor a trinomial. (6a + -5b)(3a + -2b) = 0Subproblem 1
Set the factor '(6a + -5b)' equal to zero and attempt to solve: Simplifying 6a + -5b = 0 Solving 6a + -5b = 0 Move all terms containing a to the left, all other terms to the right. Add '5b' to each side of the equation. 6a + -5b + 5b = 0 + 5b Combine like terms: -5b + 5b = 0 6a + 0 = 0 + 5b 6a = 0 + 5b Remove the zero: 6a = 5b Divide each side by '6'. a = 0.8333333333b Simplifying a = 0.8333333333bSubproblem 2
Set the factor '(3a + -2b)' equal to zero and attempt to solve: Simplifying 3a + -2b = 0 Solving 3a + -2b = 0 Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. 3a + -2b + 2b = 0 + 2b Combine like terms: -2b + 2b = 0 3a + 0 = 0 + 2b 3a = 0 + 2b Remove the zero: 3a = 2b Divide each side by '3'. a = 0.6666666667b Simplifying a = 0.6666666667bSolution
a = {0.8333333333b, 0.6666666667b}
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