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Simplifying 17c2 + 6c = 8c + -3c2 Reorder the terms: 6c + 17c2 = 8c + -3c2 Solving 6c + 17c2 = 8c + -3c2 Solving for variable 'c'. Reorder the terms: 6c + -8c + 17c2 + 3c2 = 8c + -3c2 + -8c + 3c2 Combine like terms: 6c + -8c = -2c -2c + 17c2 + 3c2 = 8c + -3c2 + -8c + 3c2 Combine like terms: 17c2 + 3c2 = 20c2 -2c + 20c2 = 8c + -3c2 + -8c + 3c2 Reorder the terms: -2c + 20c2 = 8c + -8c + -3c2 + 3c2 Combine like terms: 8c + -8c = 0 -2c + 20c2 = 0 + -3c2 + 3c2 -2c + 20c2 = -3c2 + 3c2 Combine like terms: -3c2 + 3c2 = 0 -2c + 20c2 = 0 Factor out the Greatest Common Factor (GCF), '2c'. 2c(-1 + 10c) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'c' equal to zero and attempt to solve: Simplifying c = 0 Solving c = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c = 0Subproblem 2
Set the factor '(-1 + 10c)' equal to zero and attempt to solve: Simplifying -1 + 10c = 0 Solving -1 + 10c = 0 Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 10c = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 10c = 0 + 1 10c = 0 + 1 Combine like terms: 0 + 1 = 1 10c = 1 Divide each side by '10'. c = 0.1 Simplifying c = 0.1Solution
c = {0, 0.1}
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