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Simplifying 8c2 + 48c + -1296 = 0 Reorder the terms: -1296 + 48c + 8c2 = 0 Solving -1296 + 48c + 8c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '8'. 8(-162 + 6c + c2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-162 + 6c + c2)' equal to zero and attempt to solve: Simplifying -162 + 6c + c2 = 0 Solving -162 + 6c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '162' to each side of the equation. -162 + 6c + 162 + c2 = 0 + 162 Reorder the terms: -162 + 162 + 6c + c2 = 0 + 162 Combine like terms: -162 + 162 = 0 0 + 6c + c2 = 0 + 162 6c + c2 = 0 + 162 Combine like terms: 0 + 162 = 162 6c + c2 = 162 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 = 162 + 9 Reorder the terms: 9 + 6c + c2 = 162 + 9 Combine like terms: 162 + 9 = 171 9 + 6c + c2 = 171 Factor a perfect square on the left side: (c + 3)(c + 3) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (c + 3) equal to 13.076696831 and -13.076696831.Subproblem 1
c + 3 = 13.076696831 Simplifying c + 3 = 13.076696831 Reorder the terms: 3 + c = 13.076696831 Solving 3 + c = 13.076696831 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 = 13.076696831 + -3 Combine like terms: 3 + -3 = 0 0 + c = 13.076696831 + -3 c = 13.076696831 + -3 Combine like terms: 13.076696831 + -3 = 10.076696831 c = 10.076696831 Simplifying c = 10.076696831Subproblem 2
c + 3 = -13.076696831 Simplifying c + 3 = -13.076696831 Reorder the terms: 3 + c = -13.076696831 Solving 3 + c = -13.076696831 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 = -13.076696831 + -3 Combine like terms: 3 + -3 = 0 0 + c = -13.076696831 + -3 c = -13.076696831 + -3 Combine like terms: -13.076696831 + -3 = -16.076696831 c = -16.076696831 Simplifying c = -16.076696831Solution
The solution to the problem is based on the solutions from the subproblems. c = {10.076696831, -16.076696831}Solution
c = {10.076696831, -16.076696831}
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