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Simplifying 12a2 + 5ab + -2b2 = 0 Reorder the terms: 5ab + 12a2 + -2b2 = 0 Solving 5ab + 12a2 + -2b2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + -1b)(3a + 2b) = 0Subproblem 1
Set the factor '(4a + -1b)' equal to zero and attempt to solve: Simplifying 4a + -1b = 0 Solving 4a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 4a + -1b + b = 0 + b Combine like terms: -1b + b = 0 4a + 0 = 0 + b 4a = 0 + b Remove the zero: 4a = b Divide each side by '4'. a = 0.25b Simplifying a = 0.25bSubproblem 2
Set the factor '(3a + 2b)' equal to zero and attempt to solve: Simplifying 3a + 2b = 0 Solving 3a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 3a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 3a + 0 = 0 + -2b 3a = 0 + -2b Remove the zero: 3a = -2b Divide each side by '3'. a = -0.6666666667b Simplifying a = -0.6666666667bSolution
a = {0.25b, -0.6666666667b}
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