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Simplifying 10c2 + -33cr + 20r2 = 0 Reorder the terms: -33cr + 10c2 + 20r2 = 0 Solving -33cr + 10c2 + 20r2 = 0 Solving for variable 'c'. Factor a trinomial. (2c + -5r)(5c + -4r) = 0Subproblem 1
Set the factor '(2c + -5r)' equal to zero and attempt to solve: Simplifying 2c + -5r = 0 Solving 2c + -5r = 0 Move all terms containing c to the left, all other terms to the right. Add '5r' to each side of the equation. 2c + -5r + 5r = 0 + 5r Combine like terms: -5r + 5r = 0 2c + 0 = 0 + 5r 2c = 0 + 5r Remove the zero: 2c = 5r Divide each side by '2'. c = 2.5r Simplifying c = 2.5rSubproblem 2
Set the factor '(5c + -4r)' equal to zero and attempt to solve: Simplifying 5c + -4r = 0 Solving 5c + -4r = 0 Move all terms containing c to the left, all other terms to the right. Add '4r' to each side of the equation. 5c + -4r + 4r = 0 + 4r Combine like terms: -4r + 4r = 0 5c + 0 = 0 + 4r 5c = 0 + 4r Remove the zero: 5c = 4r Divide each side by '5'. c = 0.8r Simplifying c = 0.8rSolution
c = {2.5r, 0.8r}
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