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Simplifying 20b2 + 13ba + -15a2 = 0 Reorder the terms: 13ab + -15a2 + 20b2 = 0 Solving 13ab + -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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