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Simplifying (10c2 + -33cd + 20d2) = 0 Reorder the terms: (-33cd + 10c2 + 20d2) = 0 Remove parenthesis around (-33cd + 10c2 + 20d2) -33cd + 10c2 + 20d2 = 0 Solving -33cd + 10c2 + 20d2 = 0 Solving for variable 'c'. Factor a trinomial. (2c + -5d)(5c + -4d) = 0Subproblem 1
Set the factor '(2c + -5d)' equal to zero and attempt to solve: Simplifying 2c + -5d = 0 Solving 2c + -5d = 0 Move all terms containing c to the left, all other terms to the right. Add '5d' to each side of the equation. 2c + -5d + 5d = 0 + 5d Combine like terms: -5d + 5d = 0 2c + 0 = 0 + 5d 2c = 0 + 5d Remove the zero: 2c = 5d Divide each side by '2'. c = 2.5d Simplifying c = 2.5dSubproblem 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 = {2.5d, 0.8d}
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