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Simplifying 24a2 + 19ab + 2b2 = 0 Reorder the terms: 19ab + 24a2 + 2b2 = 0 Solving 19ab + 24a2 + 2b2 = 0 Solving for variable 'a'. Factor a trinomial. (8a + b)(3a + 2b) = 0Subproblem 1
Set the factor '(8a + b)' equal to zero and attempt to solve: Simplifying 8a + b = 0 Solving 8a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 8a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 8a + 0 = 0 + -1b 8a = 0 + -1b Remove the zero: 8a = -1b Divide each side by '8'. a = -0.125b Simplifying a = -0.125bSubproblem 2
Set the factor '(3a + 2b)' equal to zero and attempt to solve: Simplifying 3a + 2b = 0 Solving 3a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 3a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 3a + 0 = 0 + -2b 3a = 0 + -2b Remove the zero: 3a = -2b Divide each side by '3'. a = -0.6666666667b Simplifying a = -0.6666666667bSolution
a = {-0.125b, -0.6666666667b}
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