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Simplifying (10a2 + 18b2 + -27ab) = 0 Reorder the terms: (-27ab + 10a2 + 18b2) = 0 Remove parenthesis around (-27ab + 10a2 + 18b2) -27ab + 10a2 + 18b2 = 0 Solving -27ab + 10a2 + 18b2 = 0 Solving for variable 'a'. Factor a trinomial. (2a + -3b)(5a + -6b) = 0Subproblem 1
Set the factor '(2a + -3b)' equal to zero and attempt to solve: Simplifying 2a + -3b = 0 Solving 2a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 2a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 2a + 0 = 0 + 3b 2a = 0 + 3b Remove the zero: 2a = 3b Divide each side by '2'. a = 1.5b Simplifying a = 1.5bSubproblem 2
Set the factor '(5a + -6b)' equal to zero and attempt to solve: Simplifying 5a + -6b = 0 Solving 5a + -6b = 0 Move all terms containing a to the left, all other terms to the right. Add '6b' to each side of the equation. 5a + -6b + 6b = 0 + 6b Combine like terms: -6b + 6b = 0 5a + 0 = 0 + 6b 5a = 0 + 6b Remove the zero: 5a = 6b Divide each side by '5'. a = 1.2b Simplifying a = 1.2bSolution
a = {1.5b, 1.2b}
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