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Simplifying 3(4c + 1) * 2c = 13 Reorder the terms: 3(1 + 4c) * 2c = 13 Reorder the terms for easier multiplication: 3 * 2c(1 + 4c) = 13 Multiply 3 * 2 6c(1 + 4c) = 13 (1 * 6c + 4c * 6c) = 13 (6c + 24c2) = 13 Solving 6c + 24c2 = 13 Solving for variable 'c'. Reorder the terms: -13 + 6c + 24c2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 6c + 24c2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.5416666667 + 0.25c + c2 = 0 Move the constant term to the right: Add '0.5416666667' to each side of the equation. -0.5416666667 + 0.25c + 0.5416666667 + c2 = 0 + 0.5416666667 Reorder the terms: -0.5416666667 + 0.5416666667 + 0.25c + c2 = 0 + 0.5416666667 Combine like terms: -0.5416666667 + 0.5416666667 = 0.0000000000 0.0000000000 + 0.25c + c2 = 0 + 0.5416666667 0.25c + c2 = 0 + 0.5416666667 Combine like terms: 0 + 0.5416666667 = 0.5416666667 0.25c + c2 = 0.5416666667 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 = 0.5416666667 + 0.015625 Reorder the terms: 0.015625 + 0.25c + c2 = 0.5416666667 + 0.015625 Combine like terms: 0.5416666667 + 0.015625 = 0.5572916667 0.015625 + 0.25c + c2 = 0.5572916667 Factor a perfect square on the left side: (c + 0.125)(c + 0.125) = 0.5572916667 Calculate the square root of the right side: 0.746519703 Break this problem into two subproblems by setting (c + 0.125) equal to 0.746519703 and -0.746519703.Subproblem 1
c + 0.125 = 0.746519703 Simplifying c + 0.125 = 0.746519703 Reorder the terms: 0.125 + c = 0.746519703 Solving 0.125 + c = 0.746519703 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 = 0.746519703 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + c = 0.746519703 + -0.125 c = 0.746519703 + -0.125 Combine like terms: 0.746519703 + -0.125 = 0.621519703 c = 0.621519703 Simplifying c = 0.621519703Subproblem 2
c + 0.125 = -0.746519703 Simplifying c + 0.125 = -0.746519703 Reorder the terms: 0.125 + c = -0.746519703 Solving 0.125 + c = -0.746519703 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 = -0.746519703 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + c = -0.746519703 + -0.125 c = -0.746519703 + -0.125 Combine like terms: -0.746519703 + -0.125 = -0.871519703 c = -0.871519703 Simplifying c = -0.871519703Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.621519703, -0.871519703}
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