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Simplifying c2 + 13ac + 12a2 = 0 Reorder the terms: 13ac + 12a2 + c2 = 0 Solving 13ac + 12a2 + c2 = 0 Solving for variable 'a'. Factor a trinomial. (12a + c)(a + c) = 0Subproblem 1
Set the factor '(12a + c)' equal to zero and attempt to solve: Simplifying 12a + c = 0 Solving 12a + c = 0 Move all terms containing a to the left, all other terms to the right. Add '-1c' to each side of the equation. 12a + c + -1c = 0 + -1c Combine like terms: c + -1c = 0 12a + 0 = 0 + -1c 12a = 0 + -1c Remove the zero: 12a = -1c Divide each side by '12'. a = -0.08333333333c Simplifying a = -0.08333333333cSubproblem 2
Set the factor '(a + c)' equal to zero and attempt to solve: Simplifying a + c = 0 Solving a + c = 0 Move all terms containing a to the left, all other terms to the right. Add '-1c' to each side of the equation. a + c + -1c = 0 + -1c Combine like terms: c + -1c = 0 a + 0 = 0 + -1c a = 0 + -1c Remove the zero: a = -1c Simplifying a = -1cSolution
a = {-0.08333333333c, -1c}
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