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Simplifying 24c3 + -22c2 + 4c = 2c Reorder the terms: 4c + -22c2 + 24c3 = 2c Solving 4c + -22c2 + 24c3 = 2c Solving for variable 'c'. Reorder the terms: 4c + -2c + -22c2 + 24c3 = 2c + -2c Combine like terms: 4c + -2c = 2c 2c + -22c2 + 24c3 = 2c + -2c Combine like terms: 2c + -2c = 0 2c + -22c2 + 24c3 = 0 Factor out the Greatest Common Factor (GCF), '2c'. 2c(1 + -11c + 12c2) = 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 + -11c + 12c2)' equal to zero and attempt to solve: Simplifying 1 + -11c + 12c2 = 0 Solving 1 + -11c + 12c2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.08333333333 + -0.9166666667c + c2 = 0 Move the constant term to the right: Add '-0.08333333333' to each side of the equation. 0.08333333333 + -0.9166666667c + -0.08333333333 + c2 = 0 + -0.08333333333 Reorder the terms: 0.08333333333 + -0.08333333333 + -0.9166666667c + c2 = 0 + -0.08333333333 Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000 0.00000000000 + -0.9166666667c + c2 = 0 + -0.08333333333 -0.9166666667c + c2 = 0 + -0.08333333333 Combine like terms: 0 + -0.08333333333 = -0.08333333333 -0.9166666667c + c2 = -0.08333333333 The c term is -0.9166666667c. Take half its coefficient (-0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. -0.9166666667c + 0.2100694445 + c2 = -0.08333333333 + 0.2100694445 Reorder the terms: 0.2100694445 + -0.9166666667c + c2 = -0.08333333333 + 0.2100694445 Combine like terms: -0.08333333333 + 0.2100694445 = 0.12673611117 0.2100694445 + -0.9166666667c + c2 = 0.12673611117 Factor a perfect square on the left side: (c + -0.4583333334)(c + -0.4583333334) = 0.12673611117 Calculate the square root of the right side: 0.356000156 Break this problem into two subproblems by setting (c + -0.4583333334) equal to 0.356000156 and -0.356000156.Subproblem 1
c + -0.4583333334 = 0.356000156 Simplifying c + -0.4583333334 = 0.356000156 Reorder the terms: -0.4583333334 + c = 0.356000156 Solving -0.4583333334 + c = 0.356000156 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.4583333334' to each side of the equation. -0.4583333334 + 0.4583333334 + c = 0.356000156 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + c = 0.356000156 + 0.4583333334 c = 0.356000156 + 0.4583333334 Combine like terms: 0.356000156 + 0.4583333334 = 0.8143334894 c = 0.8143334894 Simplifying c = 0.8143334894Subproblem 2
c + -0.4583333334 = -0.356000156 Simplifying c + -0.4583333334 = -0.356000156 Reorder the terms: -0.4583333334 + c = -0.356000156 Solving -0.4583333334 + c = -0.356000156 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.4583333334' to each side of the equation. -0.4583333334 + 0.4583333334 + c = -0.356000156 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + c = -0.356000156 + 0.4583333334 c = -0.356000156 + 0.4583333334 Combine like terms: -0.356000156 + 0.4583333334 = 0.1023331774 c = 0.1023331774 Simplifying c = 0.1023331774Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.8143334894, 0.1023331774}Solution
c = {0, 0.8143334894, 0.1023331774}
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