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Simplifying 15a2 + -5ab + -20b2 = 0 Reorder the terms: -5ab + 15a2 + -20b2 = 0 Solving -5ab + 15a2 + -20b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(-1ab + 3a2 + -4b2) = 0 Factor a trinomial. 5((3a + -4b)(a + 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 '(a + b)' equal to zero and attempt to solve: Simplifying a + b = 0 Solving a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 a + 0 = 0 + -1b a = 0 + -1b Remove the zero: a = -1b Simplifying a = -1bSolution
a = {1.333333333b, -1b}
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