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Simplifying 96a2 + -52ab + -28b2 = 0 Reorder the terms: -52ab + 96a2 + -28b2 = 0 Solving -52ab + 96a2 + -28b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-13ab + 24a2 + -7b2) = 0 Factor a trinomial. 4((8a + -7b)(3a + b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8a + -7b)' equal to zero and attempt to solve: Simplifying 8a + -7b = 0 Solving 8a + -7b = 0 Move all terms containing a to the left, all other terms to the right. Add '7b' to each side of the equation. 8a + -7b + 7b = 0 + 7b Combine like terms: -7b + 7b = 0 8a + 0 = 0 + 7b 8a = 0 + 7b Remove the zero: 8a = 7b Divide each side by '8'. a = 0.875b Simplifying a = 0.875bSubproblem 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 = {0.875b, -0.3333333333b}
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