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Simplifying 8c2 + -27c + -24 = 0 Reorder the terms: -24 + -27c + 8c2 = 0 Solving -24 + -27c + 8c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3 + -3.375c + c2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -3.375c + 3 + c2 = 0 + 3 Reorder the terms: -3 + 3 + -3.375c + c2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3.375c + c2 = 0 + 3 -3.375c + c2 = 0 + 3 Combine like terms: 0 + 3 = 3 -3.375c + c2 = 3 The c term is -3.375c. Take half its coefficient (-1.6875). Square it (2.84765625) and add it to both sides. Add '2.84765625' to each side of the equation. -3.375c + 2.84765625 + c2 = 3 + 2.84765625 Reorder the terms: 2.84765625 + -3.375c + c2 = 3 + 2.84765625 Combine like terms: 3 + 2.84765625 = 5.84765625 2.84765625 + -3.375c + c2 = 5.84765625 Factor a perfect square on the left side: (c + -1.6875)(c + -1.6875) = 5.84765625 Calculate the square root of the right side: 2.418192765 Break this problem into two subproblems by setting (c + -1.6875) equal to 2.418192765 and -2.418192765.Subproblem 1
c + -1.6875 = 2.418192765 Simplifying c + -1.6875 = 2.418192765 Reorder the terms: -1.6875 + c = 2.418192765 Solving -1.6875 + c = 2.418192765 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + c = 2.418192765 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + c = 2.418192765 + 1.6875 c = 2.418192765 + 1.6875 Combine like terms: 2.418192765 + 1.6875 = 4.105692765 c = 4.105692765 Simplifying c = 4.105692765Subproblem 2
c + -1.6875 = -2.418192765 Simplifying c + -1.6875 = -2.418192765 Reorder the terms: -1.6875 + c = -2.418192765 Solving -1.6875 + c = -2.418192765 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + c = -2.418192765 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + c = -2.418192765 + 1.6875 c = -2.418192765 + 1.6875 Combine like terms: -2.418192765 + 1.6875 = -0.730692765 c = -0.730692765 Simplifying c = -0.730692765Solution
The solution to the problem is based on the solutions from the subproblems. c = {4.105692765, -0.730692765}
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