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Simplifying 4c2 + -78 = 24c Reorder the terms: -78 + 4c2 = 24c Solving -78 + 4c2 = 24c Solving for variable 'c'. Reorder the terms: -78 + -24c + 4c2 = 24c + -24c Combine like terms: 24c + -24c = 0 -78 + -24c + 4c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-39 + -12c + 2c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-39 + -12c + 2c2)' equal to zero and attempt to solve: Simplifying -39 + -12c + 2c2 = 0 Solving -39 + -12c + 2c2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -19.5 + -6c + c2 = 0 Move the constant term to the right: Add '19.5' to each side of the equation. -19.5 + -6c + 19.5 + c2 = 0 + 19.5 Reorder the terms: -19.5 + 19.5 + -6c + c2 = 0 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + -6c + c2 = 0 + 19.5 -6c + c2 = 0 + 19.5 Combine like terms: 0 + 19.5 = 19.5 -6c + c2 = 19.5 The c term is -6c. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6c + 9 + c2 = 19.5 + 9 Reorder the terms: 9 + -6c + c2 = 19.5 + 9 Combine like terms: 19.5 + 9 = 28.5 9 + -6c + c2 = 28.5 Factor a perfect square on the left side: (c + -3)(c + -3) = 28.5 Calculate the square root of the right side: 5.338539126 Break this problem into two subproblems by setting (c + -3) equal to 5.338539126 and -5.338539126.Subproblem 1
c + -3 = 5.338539126 Simplifying c + -3 = 5.338539126 Reorder the terms: -3 + c = 5.338539126 Solving -3 + c = 5.338539126 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + c = 5.338539126 + 3 Combine like terms: -3 + 3 = 0 0 + c = 5.338539126 + 3 c = 5.338539126 + 3 Combine like terms: 5.338539126 + 3 = 8.338539126 c = 8.338539126 Simplifying c = 8.338539126Subproblem 2
c + -3 = -5.338539126 Simplifying c + -3 = -5.338539126 Reorder the terms: -3 + c = -5.338539126 Solving -3 + c = -5.338539126 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + c = -5.338539126 + 3 Combine like terms: -3 + 3 = 0 0 + c = -5.338539126 + 3 c = -5.338539126 + 3 Combine like terms: -5.338539126 + 3 = -2.338539126 c = -2.338539126 Simplifying c = -2.338539126Solution
The solution to the problem is based on the solutions from the subproblems. c = {8.338539126, -2.338539126}Solution
c = {8.338539126, -2.338539126}
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