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Simplifying 4c2 + -72 = 24c Reorder the terms: -72 + 4c2 = 24c Solving -72 + 4c2 = 24c Solving for variable 'c'. Reorder the terms: -72 + -24c + 4c2 = 24c + -24c Combine like terms: 24c + -24c = 0 -72 + -24c + 4c2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-18 + -6c + c2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-18 + -6c + c2)' equal to zero and attempt to solve: Simplifying -18 + -6c + c2 = 0 Solving -18 + -6c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -6c + 18 + c2 = 0 + 18 Reorder the terms: -18 + 18 + -6c + c2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -6c + c2 = 0 + 18 -6c + c2 = 0 + 18 Combine like terms: 0 + 18 = 18 -6c + c2 = 18 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 = 18 + 9 Reorder the terms: 9 + -6c + c2 = 18 + 9 Combine like terms: 18 + 9 = 27 9 + -6c + c2 = 27 Factor a perfect square on the left side: (c + -3)(c + -3) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (c + -3) equal to 5.196152423 and -5.196152423.Subproblem 1
c + -3 = 5.196152423 Simplifying c + -3 = 5.196152423 Reorder the terms: -3 + c = 5.196152423 Solving -3 + c = 5.196152423 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 = 5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + c = 5.196152423 + 3 c = 5.196152423 + 3 Combine like terms: 5.196152423 + 3 = 8.196152423 c = 8.196152423 Simplifying c = 8.196152423Subproblem 2
c + -3 = -5.196152423 Simplifying c + -3 = -5.196152423 Reorder the terms: -3 + c = -5.196152423 Solving -3 + c = -5.196152423 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 = -5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + c = -5.196152423 + 3 c = -5.196152423 + 3 Combine like terms: -5.196152423 + 3 = -2.196152423 c = -2.196152423 Simplifying c = -2.196152423Solution
The solution to the problem is based on the solutions from the subproblems. c = {8.196152423, -2.196152423}Solution
c = {8.196152423, -2.196152423}
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