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Simplifying 105c2 + -177c + 54 = 0 Reorder the terms: 54 + -177c + 105c2 = 0 Solving 54 + -177c + 105c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '3'. 3(18 + -59c + 35c2) = 0 Factor a trinomial. 3((2 + -5c)(9 + -7c)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -5c)' equal to zero and attempt to solve: Simplifying 2 + -5c = 0 Solving 2 + -5c = 0 Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5c = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5c = 0 + -2 -5c = 0 + -2 Combine like terms: 0 + -2 = -2 -5c = -2 Divide each side by '-5'. c = 0.4 Simplifying c = 0.4Subproblem 2
Set the factor '(9 + -7c)' equal to zero and attempt to solve: Simplifying 9 + -7c = 0 Solving 9 + -7c = 0 Move all terms containing c to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -7c = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7c = 0 + -9 -7c = 0 + -9 Combine like terms: 0 + -9 = -9 -7c = -9 Divide each side by '-7'. c = 1.285714286 Simplifying c = 1.285714286Solution
c = {0.4, 1.285714286}
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