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Simplifying (5c + 4d)(5c + 4d) = 0 Multiply (5c + 4d) * (5c + 4d) (5c * (5c + 4d) + 4d * (5c + 4d)) = 0 ((5c * 5c + 4d * 5c) + 4d * (5c + 4d)) = 0 Reorder the terms: ((20cd + 25c2) + 4d * (5c + 4d)) = 0 ((20cd + 25c2) + 4d * (5c + 4d)) = 0 (20cd + 25c2 + (5c * 4d + 4d * 4d)) = 0 (20cd + 25c2 + (20cd + 16d2)) = 0 Reorder the terms: (20cd + 20cd + 25c2 + 16d2) = 0 Combine like terms: 20cd + 20cd = 40cd (40cd + 25c2 + 16d2) = 0 Solving 40cd + 25c2 + 16d2 = 0 Solving for variable 'c'. Factor a trinomial. (5c + 4d)(5c + 4d) = 0Subproblem 1
Set the factor '(5c + 4d)' equal to zero and attempt to solve: Simplifying 5c + 4d = 0 Solving 5c + 4d = 0 Move all terms containing c to the left, all other terms to the right. Add '-4d' to each side of the equation. 5c + 4d + -4d = 0 + -4d Combine like terms: 4d + -4d = 0 5c + 0 = 0 + -4d 5c = 0 + -4d Remove the zero: 5c = -4d Divide each side by '5'. c = -0.8d Simplifying c = -0.8dSubproblem 2
Set the factor '(5c + 4d)' equal to zero and attempt to solve: Simplifying 5c + 4d = 0 Solving 5c + 4d = 0 Move all terms containing c to the left, all other terms to the right. Add '-4d' to each side of the equation. 5c + 4d + -4d = 0 + -4d Combine like terms: 4d + -4d = 0 5c + 0 = 0 + -4d 5c = 0 + -4d Remove the zero: 5c = -4d Divide each side by '5'. c = -0.8d Simplifying c = -0.8dSolution
c = {-0.8d, -0.8d}
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