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Simplifying 20a2 + -23ab + 6b2 = 0 Reorder the terms: -23ab + 20a2 + 6b2 = 0 Solving -23ab + 20a2 + 6b2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + -3b)(5a + -2b) = 0Subproblem 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 '(5a + -2b)' equal to zero and attempt to solve: Simplifying 5a + -2b = 0 Solving 5a + -2b = 0 Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. 5a + -2b + 2b = 0 + 2b Combine like terms: -2b + 2b = 0 5a + 0 = 0 + 2b 5a = 0 + 2b Remove the zero: 5a = 2b Divide each side by '5'. a = 0.4b Simplifying a = 0.4bSolution
a = {0.75b, 0.4b}
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