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Simplifying 10c2 + -21c = 14c + 6 Reorder the terms: -21c + 10c2 = 14c + 6 Reorder the terms: -21c + 10c2 = 6 + 14c Solving -21c + 10c2 = 6 + 14c Solving for variable 'c'. Reorder the terms: -6 + -21c + -14c + 10c2 = 6 + 14c + -6 + -14c Combine like terms: -21c + -14c = -35c -6 + -35c + 10c2 = 6 + 14c + -6 + -14c Reorder the terms: -6 + -35c + 10c2 = 6 + -6 + 14c + -14c Combine like terms: 6 + -6 = 0 -6 + -35c + 10c2 = 0 + 14c + -14c -6 + -35c + 10c2 = 14c + -14c Combine like terms: 14c + -14c = 0 -6 + -35c + 10c2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.6 + -3.5c + c2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -3.5c + 0.6 + c2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -3.5c + c2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -3.5c + c2 = 0 + 0.6 -3.5c + c2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -3.5c + c2 = 0.6 The c term is -3.5c. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5c + 3.0625 + c2 = 0.6 + 3.0625 Reorder the terms: 3.0625 + -3.5c + c2 = 0.6 + 3.0625 Combine like terms: 0.6 + 3.0625 = 3.6625 3.0625 + -3.5c + c2 = 3.6625 Factor a perfect square on the left side: (c + -1.75)(c + -1.75) = 3.6625 Calculate the square root of the right side: 1.913765921 Break this problem into two subproblems by setting (c + -1.75) equal to 1.913765921 and -1.913765921.Subproblem 1
c + -1.75 = 1.913765921 Simplifying c + -1.75 = 1.913765921 Reorder the terms: -1.75 + c = 1.913765921 Solving -1.75 + c = 1.913765921 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + c = 1.913765921 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + c = 1.913765921 + 1.75 c = 1.913765921 + 1.75 Combine like terms: 1.913765921 + 1.75 = 3.663765921 c = 3.663765921 Simplifying c = 3.663765921Subproblem 2
c + -1.75 = -1.913765921 Simplifying c + -1.75 = -1.913765921 Reorder the terms: -1.75 + c = -1.913765921 Solving -1.75 + c = -1.913765921 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + c = -1.913765921 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + c = -1.913765921 + 1.75 c = -1.913765921 + 1.75 Combine like terms: -1.913765921 + 1.75 = -0.163765921 c = -0.163765921 Simplifying c = -0.163765921Solution
The solution to the problem is based on the solutions from the subproblems. c = {3.663765921, -0.163765921}
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