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Simplifying 13a2 + -83ab + 30b2 = 0 Reorder the terms: -83ab + 13a2 + 30b2 = 0 Solving -83ab + 13a2 + 30b2 = 0 Solving for variable 'a'. Factor a trinomial. (a + -6b)(13a + -5b) = 0Subproblem 1
Set the factor '(a + -6b)' equal to zero and attempt to solve: Simplifying a + -6b = 0 Solving a + -6b = 0 Move all terms containing a to the left, all other terms to the right. Add '6b' to each side of the equation. a + -6b + 6b = 0 + 6b Combine like terms: -6b + 6b = 0 a + 0 = 0 + 6b a = 0 + 6b Remove the zero: a = 6b Simplifying a = 6bSubproblem 2
Set the factor '(13a + -5b)' equal to zero and attempt to solve: Simplifying 13a + -5b = 0 Solving 13a + -5b = 0 Move all terms containing a to the left, all other terms to the right. Add '5b' to each side of the equation. 13a + -5b + 5b = 0 + 5b Combine like terms: -5b + 5b = 0 13a + 0 = 0 + 5b 13a = 0 + 5b Remove the zero: 13a = 5b Divide each side by '13'. a = 0.3846153846b Simplifying a = 0.3846153846bSolution
a = {6b, 0.3846153846b}
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