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Simplifying 45a2 + -45ab + -20b2 = 0 Reorder the terms: -45ab + 45a2 + -20b2 = 0 Solving -45ab + 45a2 + -20b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(-9ab + 9a2 + -4b2) = 0 Factor a trinomial. 5((3a + -4b)(3a + b)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3a + -4b)' equal to zero and attempt to solve: Simplifying 3a + -4b = 0 Solving 3a + -4b = 0 Move all terms containing a to the left, all other terms to the right. Add '4b' to each side of the equation. 3a + -4b + 4b = 0 + 4b Combine like terms: -4b + 4b = 0 3a + 0 = 0 + 4b 3a = 0 + 4b Remove the zero: 3a = 4b Divide each side by '3'. a = 1.333333333b Simplifying a = 1.333333333bSubproblem 2
Set the factor '(3a + b)' equal to zero and attempt to solve: Simplifying 3a + b = 0 Solving 3a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 3a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 3a + 0 = 0 + -1b 3a = 0 + -1b Remove the zero: 3a = -1b Divide each side by '3'. a = -0.3333333333b Simplifying a = -0.3333333333bSolution
a = {1.333333333b, -0.3333333333b}
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