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Simplifying -2c(-2c + -12) = 2c + -12 Reorder the terms: -2c(-12 + -2c) = 2c + -12 (-12 * -2c + -2c * -2c) = 2c + -12 (24c + 4c2) = 2c + -12 Reorder the terms: 24c + 4c2 = -12 + 2c Solving 24c + 4c2 = -12 + 2c Solving for variable 'c'. Reorder the terms: 12 + 24c + -2c + 4c2 = -12 + 2c + 12 + -2c Combine like terms: 24c + -2c = 22c 12 + 22c + 4c2 = -12 + 2c + 12 + -2c Reorder the terms: 12 + 22c + 4c2 = -12 + 12 + 2c + -2c Combine like terms: -12 + 12 = 0 12 + 22c + 4c2 = 0 + 2c + -2c 12 + 22c + 4c2 = 2c + -2c Combine like terms: 2c + -2c = 0 12 + 22c + 4c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 11c + 2c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + 11c + 2c2)' equal to zero and attempt to solve: Simplifying 6 + 11c + 2c2 = 0 Solving 6 + 11c + 2c2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + 5.5c + c2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 5.5c + -3 + c2 = 0 + -3 Reorder the terms: 3 + -3 + 5.5c + c2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5.5c + c2 = 0 + -3 5.5c + c2 = 0 + -3 Combine like terms: 0 + -3 = -3 5.5c + c2 = -3 The c term is 5.5c. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5c + 7.5625 + c2 = -3 + 7.5625 Reorder the terms: 7.5625 + 5.5c + c2 = -3 + 7.5625 Combine like terms: -3 + 7.5625 = 4.5625 7.5625 + 5.5c + c2 = 4.5625 Factor a perfect square on the left side: (c + 2.75)(c + 2.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (c + 2.75) equal to 2.136000936 and -2.136000936.Subproblem 1
c + 2.75 = 2.136000936 Simplifying c + 2.75 = 2.136000936 Reorder the terms: 2.75 + c = 2.136000936 Solving 2.75 + c = 2.136000936 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + c = 2.136000936 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + c = 2.136000936 + -2.75 c = 2.136000936 + -2.75 Combine like terms: 2.136000936 + -2.75 = -0.613999064 c = -0.613999064 Simplifying c = -0.613999064Subproblem 2
c + 2.75 = -2.136000936 Simplifying c + 2.75 = -2.136000936 Reorder the terms: 2.75 + c = -2.136000936 Solving 2.75 + c = -2.136000936 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + c = -2.136000936 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + c = -2.136000936 + -2.75 c = -2.136000936 + -2.75 Combine like terms: -2.136000936 + -2.75 = -4.886000936 c = -4.886000936 Simplifying c = -4.886000936Solution
The solution to the problem is based on the solutions from the subproblems. c = {-0.613999064, -4.886000936}Solution
c = {-0.613999064, -4.886000936}
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