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Simplifying 8a2 + -12ab + -20b2 = 0 Reorder the terms: -12ab + 8a2 + -20b2 = 0 Solving -12ab + 8a2 + -20b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-3ab + 2a2 + -5b2) = 0 Factor a trinomial. 4((2a + -5b)(a + b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2a + -5b)' equal to zero and attempt to solve: Simplifying 2a + -5b = 0 Solving 2a + -5b = 0 Move all terms containing a to the left, all other terms to the right. Add '5b' to each side of the equation. 2a + -5b + 5b = 0 + 5b Combine like terms: -5b + 5b = 0 2a + 0 = 0 + 5b 2a = 0 + 5b Remove the zero: 2a = 5b Divide each side by '2'. a = 2.5b Simplifying a = 2.5bSubproblem 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 = {2.5b, -1b}
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