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Simplifying 15a2 + 37ab + 20b2 = 0 Reorder the terms: 37ab + 15a2 + 20b2 = 0 Solving 37ab + 15a2 + 20b2 = 0 Solving for variable 'a'. Factor a trinomial. (5a + 4b)(3a + 5b) = 0Subproblem 1
Set the factor '(5a + 4b)' equal to zero and attempt to solve: Simplifying 5a + 4b = 0 Solving 5a + 4b = 0 Move all terms containing a to the left, all other terms to the right. Add '-4b' to each side of the equation. 5a + 4b + -4b = 0 + -4b Combine like terms: 4b + -4b = 0 5a + 0 = 0 + -4b 5a = 0 + -4b Remove the zero: 5a = -4b Divide each side by '5'. a = -0.8b Simplifying a = -0.8bSubproblem 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 = {-0.8b, -1.666666667b}
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