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Simplifying 6c2 + -1c + -1c2 + 7c + -2 = 0 Reorder the terms: -2 + -1c + 7c + 6c2 + -1c2 = 0 Combine like terms: -1c + 7c = 6c -2 + 6c + 6c2 + -1c2 = 0 Combine like terms: 6c2 + -1c2 = 5c2 -2 + 6c + 5c2 = 0 Solving -2 + 6c + 5c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 1.2c + c2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 1.2c + 0.4 + c2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 1.2c + c2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 1.2c + c2 = 0 + 0.4 1.2c + c2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 1.2c + c2 = 0.4 The c term is 1.2c. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2c + 0.36 + c2 = 0.4 + 0.36 Reorder the terms: 0.36 + 1.2c + c2 = 0.4 + 0.36 Combine like terms: 0.4 + 0.36 = 0.76 0.36 + 1.2c + c2 = 0.76 Factor a perfect square on the left side: (c + 0.6)(c + 0.6) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (c + 0.6) equal to 0.871779789 and -0.871779789.Subproblem 1
c + 0.6 = 0.871779789 Simplifying c + 0.6 = 0.871779789 Reorder the terms: 0.6 + c = 0.871779789 Solving 0.6 + c = 0.871779789 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + c = 0.871779789 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + c = 0.871779789 + -0.6 c = 0.871779789 + -0.6 Combine like terms: 0.871779789 + -0.6 = 0.271779789 c = 0.271779789 Simplifying c = 0.271779789Subproblem 2
c + 0.6 = -0.871779789 Simplifying c + 0.6 = -0.871779789 Reorder the terms: 0.6 + c = -0.871779789 Solving 0.6 + c = -0.871779789 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + c = -0.871779789 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + c = -0.871779789 + -0.6 c = -0.871779789 + -0.6 Combine like terms: -0.871779789 + -0.6 = -1.471779789 c = -1.471779789 Simplifying c = -1.471779789Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.271779789, -1.471779789}
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