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Simplifying 10p2c2 + 7pcr = 12r2 Reorder the terms: 7cpr + 10c2p2 = 12r2 Solving 7cpr + 10c2p2 = 12r2 Solving for variable 'c'. Combine like terms: 12r2 + -12r2 = 0 7cpr + 10c2p2 + -12r2 = 0 Factor a trinomial. (5cp + -4r)(2cp + 3r) = 0Subproblem 1
Set the factor '(5cp + -4r)' equal to zero and attempt to solve: Simplifying 5cp + -4r = 0 Solving 5cp + -4r = 0 Move all terms containing c to the left, all other terms to the right. Add '4r' to each side of the equation. 5cp + -4r + 4r = 0 + 4r Combine like terms: -4r + 4r = 0 5cp + 0 = 0 + 4r 5cp = 0 + 4r Remove the zero: 5cp = 4r Divide each side by '5p'. c = 0.8p-1r Simplifying c = 0.8p-1rSubproblem 2
Set the factor '(2cp + 3r)' equal to zero and attempt to solve: Simplifying 2cp + 3r = 0 Solving 2cp + 3r = 0 Move all terms containing c to the left, all other terms to the right. Add '-3r' to each side of the equation. 2cp + 3r + -3r = 0 + -3r Combine like terms: 3r + -3r = 0 2cp + 0 = 0 + -3r 2cp = 0 + -3r Remove the zero: 2cp = -3r Divide each side by '2p'. c = -1.5p-1r Simplifying c = -1.5p-1rSolution
c = {0.8p-1r, -1.5p-1r}
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