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Simplifying 3c3 + 6c2 + -114c = 0 Reorder the terms: -114c + 6c2 + 3c3 = 0 Solving -114c + 6c2 + 3c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '3c'. 3c(-38 + 2c + c2) = 0 Ignore the factor 3.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 '(-38 + 2c + c2)' equal to zero and attempt to solve: Simplifying -38 + 2c + c2 = 0 Solving -38 + 2c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 2c + 38 + c2 = 0 + 38 Reorder the terms: -38 + 38 + 2c + c2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 2c + c2 = 0 + 38 2c + c2 = 0 + 38 Combine like terms: 0 + 38 = 38 2c + c2 = 38 The c term is 2c. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2c + 1 + c2 = 38 + 1 Reorder the terms: 1 + 2c + c2 = 38 + 1 Combine like terms: 38 + 1 = 39 1 + 2c + c2 = 39 Factor a perfect square on the left side: (c + 1)(c + 1) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (c + 1) equal to 6.244997998 and -6.244997998.Subproblem 1
c + 1 = 6.244997998 Simplifying c + 1 = 6.244997998 Reorder the terms: 1 + c = 6.244997998 Solving 1 + c = 6.244997998 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + c = 6.244997998 + -1 Combine like terms: 1 + -1 = 0 0 + c = 6.244997998 + -1 c = 6.244997998 + -1 Combine like terms: 6.244997998 + -1 = 5.244997998 c = 5.244997998 Simplifying c = 5.244997998Subproblem 2
c + 1 = -6.244997998 Simplifying c + 1 = -6.244997998 Reorder the terms: 1 + c = -6.244997998 Solving 1 + c = -6.244997998 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + c = -6.244997998 + -1 Combine like terms: 1 + -1 = 0 0 + c = -6.244997998 + -1 c = -6.244997998 + -1 Combine like terms: -6.244997998 + -1 = -7.244997998 c = -7.244997998 Simplifying c = -7.244997998Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.244997998, -7.244997998}Solution
c = {0, 5.244997998, -7.244997998}
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