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Simplifying 3a2 + 7ab + 4b2 = 0 Reorder the terms: 7ab + 3a2 + 4b2 = 0 Solving 7ab + 3a2 + 4b2 = 0 Solving for variable 'a'. Factor a trinomial. (a + b)(3a + 4b) = 0Subproblem 1
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 = -1bSubproblem 2
Set the factor '(3a + 4b)' equal to zero and attempt to solve: Simplifying 3a + 4b = 0 Solving 3a + 4b = 0 Move all terms containing a to the left, all other terms to the right. Add '-4b' to each side of the equation. 3a + 4b + -4b = 0 + -4b Combine like terms: 4b + -4b = 0 3a + 0 = 0 + -4b 3a = 0 + -4b Remove the zero: 3a = -4b Divide each side by '3'. a = -1.333333333b Simplifying a = -1.333333333bSolution
a = {-1b, -1.333333333b}
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