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Simplifying 42a2 + 17ab + -15b2 = 0 Reorder the terms: 17ab + 42a2 + -15b2 = 0 Solving 17ab + 42a2 + -15b2 = 0 Solving for variable 'a'. Factor a trinomial. (7a + -3b)(6a + 5b) = 0Subproblem 1
Set the factor '(7a + -3b)' equal to zero and attempt to solve: Simplifying 7a + -3b = 0 Solving 7a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 7a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 7a + 0 = 0 + 3b 7a = 0 + 3b Remove the zero: 7a = 3b Divide each side by '7'. a = 0.4285714286b Simplifying a = 0.4285714286bSubproblem 2
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 = -0.8333333333bSolution
a = {0.4285714286b, -0.8333333333b}
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