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Simplifying 40a2 + 57ac + 20c2 = 0 Reorder the terms: 57ac + 40a2 + 20c2 = 0 Solving 57ac + 40a2 + 20c2 = 0 Solving for variable 'a'. Factor a trinomial. (8a + 5c)(5a + 4c) = 0Subproblem 1
Set the factor '(8a + 5c)' equal to zero and attempt to solve: Simplifying 8a + 5c = 0 Solving 8a + 5c = 0 Move all terms containing a to the left, all other terms to the right. Add '-5c' to each side of the equation. 8a + 5c + -5c = 0 + -5c Combine like terms: 5c + -5c = 0 8a + 0 = 0 + -5c 8a = 0 + -5c Remove the zero: 8a = -5c Divide each side by '8'. a = -0.625c Simplifying a = -0.625cSubproblem 2
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 = -0.8cSolution
a = {-0.625c, -0.8c}
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