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Simplifying 3c2 + -16ca + 21a2 = 0 Reorder the terms: -16ac + 21a2 + 3c2 = 0 Solving -16ac + 21a2 + 3c2 = 0 Solving for variable 'a'. Factor a trinomial. (7a + -3c)(3a + -1c) = 0Subproblem 1
Set the factor '(7a + -3c)' equal to zero and attempt to solve: Simplifying 7a + -3c = 0 Solving 7a + -3c = 0 Move all terms containing a to the left, all other terms to the right. Add '3c' to each side of the equation. 7a + -3c + 3c = 0 + 3c Combine like terms: -3c + 3c = 0 7a + 0 = 0 + 3c 7a = 0 + 3c Remove the zero: 7a = 3c Divide each side by '7'. a = 0.4285714286c Simplifying a = 0.4285714286cSubproblem 2
Set the factor '(3a + -1c)' equal to zero and attempt to solve: Simplifying 3a + -1c = 0 Solving 3a + -1c = 0 Move all terms containing a to the left, all other terms to the right. Add 'c' to each side of the equation. 3a + -1c + c = 0 + c Combine like terms: -1c + c = 0 3a + 0 = 0 + c 3a = 0 + c Remove the zero: 3a = c Divide each side by '3'. a = 0.3333333333c Simplifying a = 0.3333333333cSolution
a = {0.4285714286c, 0.3333333333c}
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