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Simplifying 20c2 + 11ca + -3a2 = 0 Reorder the terms: 11ac + -3a2 + 20c2 = 0 Solving 11ac + -3a2 + 20c2 = 0 Solving for variable 'a'. Factor a trinomial. (-3a + -4c)(a + -5c) = 0Subproblem 1
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 = -1.333333333cSubproblem 2
Set the factor '(a + -5c)' equal to zero and attempt to solve: Simplifying a + -5c = 0 Solving a + -5c = 0 Move all terms containing a to the left, all other terms to the right. Add '5c' to each side of the equation. a + -5c + 5c = 0 + 5c Combine like terms: -5c + 5c = 0 a + 0 = 0 + 5c a = 0 + 5c Remove the zero: a = 5c Simplifying a = 5cSolution
a = {-1.333333333c, 5c}
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