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Simplifying 10a2 + 9ab + -9b2 = 0 Reorder the terms: 9ab + 10a2 + -9b2 = 0 Solving 9ab + 10a2 + -9b2 = 0 Solving for variable 'a'. Factor a trinomial. (5a + -3b)(2a + 3b) = 0Subproblem 1
Set the factor '(5a + -3b)' equal to zero and attempt to solve: Simplifying 5a + -3b = 0 Solving 5a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 5a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 5a + 0 = 0 + 3b 5a = 0 + 3b Remove the zero: 5a = 3b Divide each side by '5'. a = 0.6b Simplifying a = 0.6bSubproblem 2
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 = -1.5bSolution
a = {0.6b, -1.5b}
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