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Simplifying 8c2 = 12 + 30c Solving 8c2 = 12 + 30c Solving for variable 'c'. Reorder the terms: -12 + -30c + 8c2 = 12 + 30c + -12 + -30c Reorder the terms: -12 + -30c + 8c2 = 12 + -12 + 30c + -30c Combine like terms: 12 + -12 = 0 -12 + -30c + 8c2 = 0 + 30c + -30c -12 + -30c + 8c2 = 30c + -30c Combine like terms: 30c + -30c = 0 -12 + -30c + 8c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -15c + 4c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -15c + 4c2)' equal to zero and attempt to solve: Simplifying -6 + -15c + 4c2 = 0 Solving -6 + -15c + 4c2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + -3.75c + c2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -3.75c + 1.5 + c2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -3.75c + c2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -3.75c + c2 = 0 + 1.5 -3.75c + c2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -3.75c + c2 = 1.5 The c term is -3.75c. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75c + 3.515625 + c2 = 1.5 + 3.515625 Reorder the terms: 3.515625 + -3.75c + c2 = 1.5 + 3.515625 Combine like terms: 1.5 + 3.515625 = 5.015625 3.515625 + -3.75c + c2 = 5.015625 Factor a perfect square on the left side: (c + -1.875)(c + -1.875) = 5.015625 Calculate the square root of the right side: 2.239559108 Break this problem into two subproblems by setting (c + -1.875) equal to 2.239559108 and -2.239559108.Subproblem 1
c + -1.875 = 2.239559108 Simplifying c + -1.875 = 2.239559108 Reorder the terms: -1.875 + c = 2.239559108 Solving -1.875 + c = 2.239559108 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + c = 2.239559108 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + c = 2.239559108 + 1.875 c = 2.239559108 + 1.875 Combine like terms: 2.239559108 + 1.875 = 4.114559108 c = 4.114559108 Simplifying c = 4.114559108Subproblem 2
c + -1.875 = -2.239559108 Simplifying c + -1.875 = -2.239559108 Reorder the terms: -1.875 + c = -2.239559108 Solving -1.875 + c = -2.239559108 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + c = -2.239559108 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + c = -2.239559108 + 1.875 c = -2.239559108 + 1.875 Combine like terms: -2.239559108 + 1.875 = -0.364559108 c = -0.364559108 Simplifying c = -0.364559108Solution
The solution to the problem is based on the solutions from the subproblems. c = {4.114559108, -0.364559108}Solution
c = {4.114559108, -0.364559108}
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