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Simplifying 2a2 + 13ab + -24b2 = 0 Reorder the terms: 13ab + 2a2 + -24b2 = 0 Solving 13ab + 2a2 + -24b2 = 0 Solving for variable 'a'. Factor a trinomial. (2a + -3b)(a + 8b) = 0Subproblem 1
Set the factor '(2a + -3b)' equal to zero and attempt to solve: Simplifying 2a + -3b = 0 Solving 2a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 2a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 2a + 0 = 0 + 3b 2a = 0 + 3b Remove the zero: 2a = 3b Divide each side by '2'. a = 1.5b Simplifying a = 1.5bSubproblem 2
Set the factor '(a + 8b)' equal to zero and attempt to solve: Simplifying a + 8b = 0 Solving a + 8b = 0 Move all terms containing a to the left, all other terms to the right. Add '-8b' to each side of the equation. a + 8b + -8b = 0 + -8b Combine like terms: 8b + -8b = 0 a + 0 = 0 + -8b a = 0 + -8b Remove the zero: a = -8b Simplifying a = -8bSolution
a = {1.5b, -8b}
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