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Simplifying 3c2 + 8c + -9 + c + -3 + 13c2 + -5c + 9 = 0 Reorder the terms: -9 + -3 + 9 + 8c + c + -5c + 3c2 + 13c2 = 0 Combine like terms: -9 + -3 = -12 -12 + 9 + 8c + c + -5c + 3c2 + 13c2 = 0 Combine like terms: -12 + 9 = -3 -3 + 8c + c + -5c + 3c2 + 13c2 = 0 Combine like terms: 8c + c = 9c -3 + 9c + -5c + 3c2 + 13c2 = 0 Combine like terms: 9c + -5c = 4c -3 + 4c + 3c2 + 13c2 = 0 Combine like terms: 3c2 + 13c2 = 16c2 -3 + 4c + 16c2 = 0 Solving -3 + 4c + 16c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + 0.25c + c2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + 0.25c + 0.1875 + c2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + 0.25c + c2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + 0.25c + c2 = 0 + 0.1875 0.25c + c2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 0.25c + c2 = 0.1875 The c term is 0.25c. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25c + 0.015625 + c2 = 0.1875 + 0.015625 Reorder the terms: 0.015625 + 0.25c + c2 = 0.1875 + 0.015625 Combine like terms: 0.1875 + 0.015625 = 0.203125 0.015625 + 0.25c + c2 = 0.203125 Factor a perfect square on the left side: (c + 0.125)(c + 0.125) = 0.203125 Calculate the square root of the right side: 0.450693909 Break this problem into two subproblems by setting (c + 0.125) equal to 0.450693909 and -0.450693909.Subproblem 1
c + 0.125 = 0.450693909 Simplifying c + 0.125 = 0.450693909 Reorder the terms: 0.125 + c = 0.450693909 Solving 0.125 + c = 0.450693909 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + c = 0.450693909 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + c = 0.450693909 + -0.125 c = 0.450693909 + -0.125 Combine like terms: 0.450693909 + -0.125 = 0.325693909 c = 0.325693909 Simplifying c = 0.325693909Subproblem 2
c + 0.125 = -0.450693909 Simplifying c + 0.125 = -0.450693909 Reorder the terms: 0.125 + c = -0.450693909 Solving 0.125 + c = -0.450693909 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + c = -0.450693909 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + c = -0.450693909 + -0.125 c = -0.450693909 + -0.125 Combine like terms: -0.450693909 + -0.125 = -0.575693909 c = -0.575693909 Simplifying c = -0.575693909Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.325693909, -0.575693909}
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