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Simplifying 8a2 + 13ab + 5b2 = 0 Reorder the terms: 13ab + 8a2 + 5b2 = 0 Solving 13ab + 8a2 + 5b2 = 0 Solving for variable 'a'. Factor a trinomial. (8a + 5b)(a + b) = 0Subproblem 1
Set the factor '(8a + 5b)' equal to zero and attempt to solve: Simplifying 8a + 5b = 0 Solving 8a + 5b = 0 Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. 8a + 5b + -5b = 0 + -5b Combine like terms: 5b + -5b = 0 8a + 0 = 0 + -5b 8a = 0 + -5b Remove the zero: 8a = -5b Divide each side by '8'. a = -0.625b Simplifying a = -0.625bSubproblem 2
Set the factor '(a + b)' equal to zero and attempt to solve: Simplifying a + b = 0 Solving a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 a + 0 = 0 + -1b a = 0 + -1b Remove the zero: a = -1b Simplifying a = -1bSolution
a = {-0.625b, -1b}
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