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Simplifying 11c3 + 34c2 + -6c = 0 Reorder the terms: -6c + 34c2 + 11c3 = 0 Solving -6c + 34c2 + 11c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), 'c'. c(-6 + 34c + 11c2) = 0Subproblem 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 '(-6 + 34c + 11c2)' equal to zero and attempt to solve: Simplifying -6 + 34c + 11c2 = 0 Solving -6 + 34c + 11c2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.5454545455 + 3.090909091c + c2 = 0 Move the constant term to the right: Add '0.5454545455' to each side of the equation. -0.5454545455 + 3.090909091c + 0.5454545455 + c2 = 0 + 0.5454545455 Reorder the terms: -0.5454545455 + 0.5454545455 + 3.090909091c + c2 = 0 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + 3.090909091c + c2 = 0 + 0.5454545455 3.090909091c + c2 = 0 + 0.5454545455 Combine like terms: 0 + 0.5454545455 = 0.5454545455 3.090909091c + c2 = 0.5454545455 The c term is 3.090909091c. Take half its coefficient (1.545454546). Square it (2.388429754) and add it to both sides. Add '2.388429754' to each side of the equation. 3.090909091c + 2.388429754 + c2 = 0.5454545455 + 2.388429754 Reorder the terms: 2.388429754 + 3.090909091c + c2 = 0.5454545455 + 2.388429754 Combine like terms: 0.5454545455 + 2.388429754 = 2.9338842995 2.388429754 + 3.090909091c + c2 = 2.9338842995 Factor a perfect square on the left side: (c + 1.545454546)(c + 1.545454546) = 2.9338842995 Calculate the square root of the right side: 1.712858517 Break this problem into two subproblems by setting (c + 1.545454546) equal to 1.712858517 and -1.712858517.Subproblem 1
c + 1.545454546 = 1.712858517 Simplifying c + 1.545454546 = 1.712858517 Reorder the terms: 1.545454546 + c = 1.712858517 Solving 1.545454546 + c = 1.712858517 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.545454546' to each side of the equation. 1.545454546 + -1.545454546 + c = 1.712858517 + -1.545454546 Combine like terms: 1.545454546 + -1.545454546 = 0.000000000 0.000000000 + c = 1.712858517 + -1.545454546 c = 1.712858517 + -1.545454546 Combine like terms: 1.712858517 + -1.545454546 = 0.167403971 c = 0.167403971 Simplifying c = 0.167403971Subproblem 2
c + 1.545454546 = -1.712858517 Simplifying c + 1.545454546 = -1.712858517 Reorder the terms: 1.545454546 + c = -1.712858517 Solving 1.545454546 + c = -1.712858517 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.545454546' to each side of the equation. 1.545454546 + -1.545454546 + c = -1.712858517 + -1.545454546 Combine like terms: 1.545454546 + -1.545454546 = 0.000000000 0.000000000 + c = -1.712858517 + -1.545454546 c = -1.712858517 + -1.545454546 Combine like terms: -1.712858517 + -1.545454546 = -3.258313063 c = -3.258313063 Simplifying c = -3.258313063Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.167403971, -3.258313063}Solution
c = {0, 0.167403971, -3.258313063}
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