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Simplifying 84c2 + -34cr + -30r2 = 0 Reorder the terms: -34cr + 84c2 + -30r2 = 0 Solving -34cr + 84c2 + -30r2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(-17cr + 42c2 + -15r2) = 0 Factor a trinomial. 2((6c + -5r)(7c + 3r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6c + -5r)' equal to zero and attempt to solve: Simplifying 6c + -5r = 0 Solving 6c + -5r = 0 Move all terms containing c to the left, all other terms to the right. Add '5r' to each side of the equation. 6c + -5r + 5r = 0 + 5r Combine like terms: -5r + 5r = 0 6c + 0 = 0 + 5r 6c = 0 + 5r Remove the zero: 6c = 5r Divide each side by '6'. c = 0.8333333333r Simplifying c = 0.8333333333rSubproblem 2
Set the factor '(7c + 3r)' equal to zero and attempt to solve: Simplifying 7c + 3r = 0 Solving 7c + 3r = 0 Move all terms containing c to the left, all other terms to the right. Add '-3r' to each side of the equation. 7c + 3r + -3r = 0 + -3r Combine like terms: 3r + -3r = 0 7c + 0 = 0 + -3r 7c = 0 + -3r Remove the zero: 7c = -3r Divide each side by '7'. c = -0.4285714286r Simplifying c = -0.4285714286rSolution
c = {0.8333333333r, -0.4285714286r}
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