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Simplifying (7c * 8c) + -3c = 10 Reorder the terms for easier multiplication: (7 * 8c * c) + -3c = 10 Multiply 7 * 8 (56c * c) + -3c = 10 Multiply c * c (56c2) + -3c = 10 Reorder the terms: -3c + (56c2) = 10 Solving -3c + (56c2) = 10 Solving for variable 'c'. Reorder the terms: -10 + -3c + (56c2) = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -3c + (56c2) = 0 Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. -0.1785714286 + -0.05357142857c + c2 = 0 Move the constant term to the right: Add '0.1785714286' to each side of the equation. -0.1785714286 + -0.05357142857c + 0.1785714286 + c2 = 0 + 0.1785714286 Reorder the terms: -0.1785714286 + 0.1785714286 + -0.05357142857c + c2 = 0 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + -0.05357142857c + c2 = 0 + 0.1785714286 -0.05357142857c + c2 = 0 + 0.1785714286 Combine like terms: 0 + 0.1785714286 = 0.1785714286 -0.05357142857c + c2 = 0.1785714286 The c term is -0.05357142857c. Take half its coefficient (-0.02678571429). Square it (0.0007174744900) and add it to both sides. Add '0.0007174744900' to each side of the equation. -0.05357142857c + 0.0007174744900 + c2 = 0.1785714286 + 0.0007174744900 Reorder the terms: 0.0007174744900 + -0.05357142857c + c2 = 0.1785714286 + 0.0007174744900 Combine like terms: 0.1785714286 + 0.0007174744900 = 0.17928890309 0.0007174744900 + -0.05357142857c + c2 = 0.17928890309 Factor a perfect square on the left side: ((c) + -0.02678571429)((c) + -0.02678571429) = 0.17928890309 Calculate the square root of the right side: 0.423425204 Break this problem into two subproblems by setting ((c) + -0.02678571429) equal to 0.423425204 and -0.423425204.Subproblem 1
(c) + -0.02678571429 = 0.423425204 Simplifying (c) + -0.02678571429 = 0.423425204 c + -0.02678571429 = 0.423425204 Reorder the terms: -0.02678571429 + c = 0.423425204 Solving -0.02678571429 + c = 0.423425204 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.02678571429' to each side of the equation. -0.02678571429 + 0.02678571429 + c = 0.423425204 + 0.02678571429 Combine like terms: -0.02678571429 + 0.02678571429 = 0.00000000000 0.00000000000 + c = 0.423425204 + 0.02678571429 c = 0.423425204 + 0.02678571429 Combine like terms: 0.423425204 + 0.02678571429 = 0.45021091829 c = 0.45021091829 Simplifying c = 0.45021091829Subproblem 2
(c) + -0.02678571429 = -0.423425204 Simplifying (c) + -0.02678571429 = -0.423425204 c + -0.02678571429 = -0.423425204 Reorder the terms: -0.02678571429 + c = -0.423425204 Solving -0.02678571429 + c = -0.423425204 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.02678571429' to each side of the equation. -0.02678571429 + 0.02678571429 + c = -0.423425204 + 0.02678571429 Combine like terms: -0.02678571429 + 0.02678571429 = 0.00000000000 0.00000000000 + c = -0.423425204 + 0.02678571429 c = -0.423425204 + 0.02678571429 Combine like terms: -0.423425204 + 0.02678571429 = -0.39663948971 c = -0.39663948971 Simplifying c = -0.39663948971Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.45021091829, -0.39663948971}
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