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Simplifying 20c2 + 13ca + -15a2 = 0 Reorder the terms: 13ac + -15a2 + 20c2 = 0 Solving 13ac + -15a2 + 20c2 = 0 Solving for variable 'a'. Factor a trinomial. (-5a + -4c)(3a + -5c) = 0Subproblem 1
Set the factor '(-5a + -4c)' equal to zero and attempt to solve: Simplifying -5a + -4c = 0 Solving -5a + -4c = 0 Move all terms containing a to the left, all other terms to the right. Add '4c' to each side of the equation. -5a + -4c + 4c = 0 + 4c Combine like terms: -4c + 4c = 0 -5a + 0 = 0 + 4c -5a = 0 + 4c Remove the zero: -5a = 4c Divide each side by '-5'. a = -0.8c Simplifying a = -0.8cSubproblem 2
Set the factor '(3a + -5c)' equal to zero and attempt to solve: Simplifying 3a + -5c = 0 Solving 3a + -5c = 0 Move all terms containing a to the left, all other terms to the right. Add '5c' to each side of the equation. 3a + -5c + 5c = 0 + 5c Combine like terms: -5c + 5c = 0 3a + 0 = 0 + 5c 3a = 0 + 5c Remove the zero: 3a = 5c Divide each side by '3'. a = 1.666666667c Simplifying a = 1.666666667cSolution
a = {-0.8c, 1.666666667c}
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