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Simplifying 18a2 + 21ac + -4c2 = 0 Reorder the terms: 21ac + 18a2 + -4c2 = 0 Solving 21ac + 18a2 + -4c2 = 0 Solving for variable 'a'. Factor a trinomial. (6a + -1c)(3a + 4c) = 0Subproblem 1
Set the factor '(6a + -1c)' equal to zero and attempt to solve: Simplifying 6a + -1c = 0 Solving 6a + -1c = 0 Move all terms containing a to the left, all other terms to the right. Add 'c' to each side of the equation. 6a + -1c + c = 0 + c Combine like terms: -1c + c = 0 6a + 0 = 0 + c 6a = 0 + c Remove the zero: 6a = c Divide each side by '6'. a = 0.1666666667c Simplifying a = 0.1666666667cSubproblem 2
Set the factor '(3a + 4c)' equal to zero and attempt to solve: Simplifying 3a + 4c = 0 Solving 3a + 4c = 0 Move all terms containing a to the left, all other terms to the right. Add '-4c' to each side of the equation. 3a + 4c + -4c = 0 + -4c Combine like terms: 4c + -4c = 0 3a + 0 = 0 + -4c 3a = 0 + -4c Remove the zero: 3a = -4c Divide each side by '3'. a = -1.333333333c Simplifying a = -1.333333333cSolution
a = {0.1666666667c, -1.333333333c}
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