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Simplifying 4c(6c + -3) = 92 Reorder the terms: 4c(-3 + 6c) = 92 (-3 * 4c + 6c * 4c) = 92 (-12c + 24c2) = 92 Solving -12c + 24c2 = 92 Solving for variable 'c'. Reorder the terms: -92 + -12c + 24c2 = 92 + -92 Combine like terms: 92 + -92 = 0 -92 + -12c + 24c2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-23 + -3c + 6c2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-23 + -3c + 6c2)' equal to zero and attempt to solve: Simplifying -23 + -3c + 6c2 = 0 Solving -23 + -3c + 6c2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.833333333 + -0.5c + c2 = 0 Move the constant term to the right: Add '3.833333333' to each side of the equation. -3.833333333 + -0.5c + 3.833333333 + c2 = 0 + 3.833333333 Reorder the terms: -3.833333333 + 3.833333333 + -0.5c + c2 = 0 + 3.833333333 Combine like terms: -3.833333333 + 3.833333333 = 0.000000000 0.000000000 + -0.5c + c2 = 0 + 3.833333333 -0.5c + c2 = 0 + 3.833333333 Combine like terms: 0 + 3.833333333 = 3.833333333 -0.5c + c2 = 3.833333333 The c term is -0.5c. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5c + 0.0625 + c2 = 3.833333333 + 0.0625 Reorder the terms: 0.0625 + -0.5c + c2 = 3.833333333 + 0.0625 Combine like terms: 3.833333333 + 0.0625 = 3.895833333 0.0625 + -0.5c + c2 = 3.895833333 Factor a perfect square on the left side: (c + -0.25)(c + -0.25) = 3.895833333 Calculate the square root of the right side: 1.973786547 Break this problem into two subproblems by setting (c + -0.25) equal to 1.973786547 and -1.973786547.Subproblem 1
c + -0.25 = 1.973786547 Simplifying c + -0.25 = 1.973786547 Reorder the terms: -0.25 + c = 1.973786547 Solving -0.25 + c = 1.973786547 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + c = 1.973786547 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + c = 1.973786547 + 0.25 c = 1.973786547 + 0.25 Combine like terms: 1.973786547 + 0.25 = 2.223786547 c = 2.223786547 Simplifying c = 2.223786547Subproblem 2
c + -0.25 = -1.973786547 Simplifying c + -0.25 = -1.973786547 Reorder the terms: -0.25 + c = -1.973786547 Solving -0.25 + c = -1.973786547 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + c = -1.973786547 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + c = -1.973786547 + 0.25 c = -1.973786547 + 0.25 Combine like terms: -1.973786547 + 0.25 = -1.723786547 c = -1.723786547 Simplifying c = -1.723786547Solution
The solution to the problem is based on the solutions from the subproblems. c = {2.223786547, -1.723786547}Solution
c = {2.223786547, -1.723786547}
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