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Simplifying 72c2 + -132cd + 56d2 = 0 Reorder the terms: -132cd + 72c2 + 56d2 = 0 Solving -132cd + 72c2 + 56d2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '4'. 4(-33cd + 18c2 + 14d2) = 0 Factor a trinomial. 4((6c + -7d)(3c + -2d)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(6c + -7d)' equal to zero and attempt to solve: Simplifying 6c + -7d = 0 Solving 6c + -7d = 0 Move all terms containing c to the left, all other terms to the right. Add '7d' to each side of the equation. 6c + -7d + 7d = 0 + 7d Combine like terms: -7d + 7d = 0 6c + 0 = 0 + 7d 6c = 0 + 7d Remove the zero: 6c = 7d Divide each side by '6'. c = 1.166666667d Simplifying c = 1.166666667dSubproblem 2
Set the factor '(3c + -2d)' equal to zero and attempt to solve: Simplifying 3c + -2d = 0 Solving 3c + -2d = 0 Move all terms containing c to the left, all other terms to the right. Add '2d' to each side of the equation. 3c + -2d + 2d = 0 + 2d Combine like terms: -2d + 2d = 0 3c + 0 = 0 + 2d 3c = 0 + 2d Remove the zero: 3c = 2d Divide each side by '3'. c = 0.6666666667d Simplifying c = 0.6666666667dSolution
c = {1.166666667d, 0.6666666667d}
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