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Simplifying 100a2 + -140ab + 48b2 = 0 Reorder the terms: -140ab + 100a2 + 48b2 = 0 Solving -140ab + 100a2 + 48b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-35ab + 25a2 + 12b2) = 0 Factor a trinomial. 4((5a + -4b)(5a + -3b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5a + -4b)' equal to zero and attempt to solve: Simplifying 5a + -4b = 0 Solving 5a + -4b = 0 Move all terms containing a to the left, all other terms to the right. Add '4b' to each side of the equation. 5a + -4b + 4b = 0 + 4b Combine like terms: -4b + 4b = 0 5a + 0 = 0 + 4b 5a = 0 + 4b Remove the zero: 5a = 4b Divide each side by '5'. a = 0.8b Simplifying a = 0.8bSubproblem 2
Set the factor '(5a + -3b)' equal to zero and attempt to solve: Simplifying 5a + -3b = 0 Solving 5a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 5a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 5a + 0 = 0 + 3b 5a = 0 + 3b Remove the zero: 5a = 3b Divide each side by '5'. a = 0.6b Simplifying a = 0.6bSolution
a = {0.8b, 0.6b}
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