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Simplifying 56a2 + -14ab + -21b2 = 0 Reorder the terms: -14ab + 56a2 + -21b2 = 0 Solving -14ab + 56a2 + -21b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '7'. 7(-2ab + 8a2 + -3b2) = 0 Factor a trinomial. 7((4a + -3b)(2a + b)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(4a + -3b)' equal to zero and attempt to solve: Simplifying 4a + -3b = 0 Solving 4a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 4a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 4a + 0 = 0 + 3b 4a = 0 + 3b Remove the zero: 4a = 3b Divide each side by '4'. a = 0.75b Simplifying a = 0.75bSubproblem 2
Set the factor '(2a + b)' equal to zero and attempt to solve: Simplifying 2a + b = 0 Solving 2a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 2a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 2a + 0 = 0 + -1b 2a = 0 + -1b Remove the zero: 2a = -1b Divide each side by '2'. a = -0.5b Simplifying a = -0.5bSolution
a = {0.75b, -0.5b}
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