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Simplifying c = 6c2 + -5c + -4 Reorder the terms: c = -4 + -5c + 6c2 Solving c = -4 + -5c + 6c2 Solving for variable 'c'. Reorder the terms: 4 + c + 5c + -6c2 = -4 + -5c + 6c2 + 4 + 5c + -6c2 Combine like terms: c + 5c = 6c 4 + 6c + -6c2 = -4 + -5c + 6c2 + 4 + 5c + -6c2 Reorder the terms: 4 + 6c + -6c2 = -4 + 4 + -5c + 5c + 6c2 + -6c2 Combine like terms: -4 + 4 = 0 4 + 6c + -6c2 = 0 + -5c + 5c + 6c2 + -6c2 4 + 6c + -6c2 = -5c + 5c + 6c2 + -6c2 Combine like terms: -5c + 5c = 0 4 + 6c + -6c2 = 0 + 6c2 + -6c2 4 + 6c + -6c2 = 6c2 + -6c2 Combine like terms: 6c2 + -6c2 = 0 4 + 6c + -6c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 3c + -3c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 3c + -3c2)' equal to zero and attempt to solve: Simplifying 2 + 3c + -3c2 = 0 Solving 2 + 3c + -3c2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.6666666667 + -1c + c2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -1c + 0.6666666667 + c2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -1c + c2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -1c + c2 = 0 + 0.6666666667 -1c + c2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -1c + c2 = 0.6666666667 The c term is -1c. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1c + 0.25 + c2 = 0.6666666667 + 0.25 Reorder the terms: 0.25 + -1c + c2 = 0.6666666667 + 0.25 Combine like terms: 0.6666666667 + 0.25 = 0.9166666667 0.25 + -1c + c2 = 0.9166666667 Factor a perfect square on the left side: (c + -0.5)(c + -0.5) = 0.9166666667 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (c + -0.5) equal to 0.957427108 and -0.957427108.Subproblem 1
c + -0.5 = 0.957427108 Simplifying c + -0.5 = 0.957427108 Reorder the terms: -0.5 + c = 0.957427108 Solving -0.5 + c = 0.957427108 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + c = 0.957427108 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = 0.957427108 + 0.5 c = 0.957427108 + 0.5 Combine like terms: 0.957427108 + 0.5 = 1.457427108 c = 1.457427108 Simplifying c = 1.457427108Subproblem 2
c + -0.5 = -0.957427108 Simplifying c + -0.5 = -0.957427108 Reorder the terms: -0.5 + c = -0.957427108 Solving -0.5 + c = -0.957427108 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + c = -0.957427108 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = -0.957427108 + 0.5 c = -0.957427108 + 0.5 Combine like terms: -0.957427108 + 0.5 = -0.457427108 c = -0.457427108 Simplifying c = -0.457427108Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.457427108, -0.457427108}Solution
c = {1.457427108, -0.457427108}
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