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Simplifying 3c2 + -24c + -256 = 0 Reorder the terms: -256 + -24c + 3c2 = 0 Solving -256 + -24c + 3c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -85.33333333 + -8c + c2 = 0 Move the constant term to the right: Add '85.33333333' to each side of the equation. -85.33333333 + -8c + 85.33333333 + c2 = 0 + 85.33333333 Reorder the terms: -85.33333333 + 85.33333333 + -8c + c2 = 0 + 85.33333333 Combine like terms: -85.33333333 + 85.33333333 = 0.00000000 0.00000000 + -8c + c2 = 0 + 85.33333333 -8c + c2 = 0 + 85.33333333 Combine like terms: 0 + 85.33333333 = 85.33333333 -8c + c2 = 85.33333333 The c term is -8c. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8c + 16 + c2 = 85.33333333 + 16 Reorder the terms: 16 + -8c + c2 = 85.33333333 + 16 Combine like terms: 85.33333333 + 16 = 101.33333333 16 + -8c + c2 = 101.33333333 Factor a perfect square on the left side: (c + -4)(c + -4) = 101.33333333 Calculate the square root of the right side: 10.066445914 Break this problem into two subproblems by setting (c + -4) equal to 10.066445914 and -10.066445914.Subproblem 1
c + -4 = 10.066445914 Simplifying c + -4 = 10.066445914 Reorder the terms: -4 + c = 10.066445914 Solving -4 + c = 10.066445914 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + c = 10.066445914 + 4 Combine like terms: -4 + 4 = 0 0 + c = 10.066445914 + 4 c = 10.066445914 + 4 Combine like terms: 10.066445914 + 4 = 14.066445914 c = 14.066445914 Simplifying c = 14.066445914Subproblem 2
c + -4 = -10.066445914 Simplifying c + -4 = -10.066445914 Reorder the terms: -4 + c = -10.066445914 Solving -4 + c = -10.066445914 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + c = -10.066445914 + 4 Combine like terms: -4 + 4 = 0 0 + c = -10.066445914 + 4 c = -10.066445914 + 4 Combine like terms: -10.066445914 + 4 = -6.066445914 c = -6.066445914 Simplifying c = -6.066445914Solution
The solution to the problem is based on the solutions from the subproblems. c = {14.066445914, -6.066445914}
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