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Simplifying 6a2 + 5ab + -4b2 = 0 Reorder the terms: 5ab + 6a2 + -4b2 = 0 Solving 5ab + 6a2 + -4b2 = 0 Solving for variable 'a'. Factor a trinomial. (2a + -1b)(3a + 4b) = 0Subproblem 1
Set the factor '(2a + -1b)' equal to zero and attempt to solve: Simplifying 2a + -1b = 0 Solving 2a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 2a + -1b + b = 0 + b Combine like terms: -1b + b = 0 2a + 0 = 0 + b 2a = 0 + b Remove the zero: 2a = b Divide each side by '2'. a = 0.5b Simplifying a = 0.5bSubproblem 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 = {0.5b, -1.333333333b}
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