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Simplifying 6c2 + -24c = 80 Reorder the terms: -24c + 6c2 = 80 Solving -24c + 6c2 = 80 Solving for variable 'c'. Reorder the terms: -80 + -24c + 6c2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + -24c + 6c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-40 + -12c + 3c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-40 + -12c + 3c2)' equal to zero and attempt to solve: Simplifying -40 + -12c + 3c2 = 0 Solving -40 + -12c + 3c2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -13.33333333 + -4c + c2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + -4c + 13.33333333 + c2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + -4c + c2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + -4c + c2 = 0 + 13.33333333 -4c + c2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 -4c + c2 = 13.33333333 The c term is -4c. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4c + 4 + c2 = 13.33333333 + 4 Reorder the terms: 4 + -4c + c2 = 13.33333333 + 4 Combine like terms: 13.33333333 + 4 = 17.33333333 4 + -4c + c2 = 17.33333333 Factor a perfect square on the left side: (c + -2)(c + -2) = 17.33333333 Calculate the square root of the right side: 4.163331999 Break this problem into two subproblems by setting (c + -2) equal to 4.163331999 and -4.163331999.Subproblem 1
c + -2 = 4.163331999 Simplifying c + -2 = 4.163331999 Reorder the terms: -2 + c = 4.163331999 Solving -2 + c = 4.163331999 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c = 4.163331999 + 2 Combine like terms: -2 + 2 = 0 0 + c = 4.163331999 + 2 c = 4.163331999 + 2 Combine like terms: 4.163331999 + 2 = 6.163331999 c = 6.163331999 Simplifying c = 6.163331999Subproblem 2
c + -2 = -4.163331999 Simplifying c + -2 = -4.163331999 Reorder the terms: -2 + c = -4.163331999 Solving -2 + c = -4.163331999 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c = -4.163331999 + 2 Combine like terms: -2 + 2 = 0 0 + c = -4.163331999 + 2 c = -4.163331999 + 2 Combine like terms: -4.163331999 + 2 = -2.163331999 c = -2.163331999 Simplifying c = -2.163331999Solution
The solution to the problem is based on the solutions from the subproblems. c = {6.163331999, -2.163331999}Solution
c = {6.163331999, -2.163331999}
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