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Simplifying 10c2 + -29c + -21 = -2c + 30c + -35 Reorder the terms: -21 + -29c + 10c2 = -2c + 30c + -35 Reorder the terms: -21 + -29c + 10c2 = -35 + -2c + 30c Combine like terms: -2c + 30c = 28c -21 + -29c + 10c2 = -35 + 28c Solving -21 + -29c + 10c2 = -35 + 28c Solving for variable 'c'. Reorder the terms: -21 + 35 + -29c + -28c + 10c2 = -35 + 28c + 35 + -28c Combine like terms: -21 + 35 = 14 14 + -29c + -28c + 10c2 = -35 + 28c + 35 + -28c Combine like terms: -29c + -28c = -57c 14 + -57c + 10c2 = -35 + 28c + 35 + -28c Reorder the terms: 14 + -57c + 10c2 = -35 + 35 + 28c + -28c Combine like terms: -35 + 35 = 0 14 + -57c + 10c2 = 0 + 28c + -28c 14 + -57c + 10c2 = 28c + -28c Combine like terms: 28c + -28c = 0 14 + -57c + 10c2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.4 + -5.7c + c2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -5.7c + -1.4 + c2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -5.7c + c2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -5.7c + c2 = 0 + -1.4 -5.7c + c2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -5.7c + c2 = -1.4 The c term is -5.7c. Take half its coefficient (-2.85). Square it (8.1225) and add it to both sides. Add '8.1225' to each side of the equation. -5.7c + 8.1225 + c2 = -1.4 + 8.1225 Reorder the terms: 8.1225 + -5.7c + c2 = -1.4 + 8.1225 Combine like terms: -1.4 + 8.1225 = 6.7225 8.1225 + -5.7c + c2 = 6.7225 Factor a perfect square on the left side: (c + -2.85)(c + -2.85) = 6.7225 Calculate the square root of the right side: 2.592778432 Break this problem into two subproblems by setting (c + -2.85) equal to 2.592778432 and -2.592778432.Subproblem 1
c + -2.85 = 2.592778432 Simplifying c + -2.85 = 2.592778432 Reorder the terms: -2.85 + c = 2.592778432 Solving -2.85 + c = 2.592778432 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.85' to each side of the equation. -2.85 + 2.85 + c = 2.592778432 + 2.85 Combine like terms: -2.85 + 2.85 = 0.00 0.00 + c = 2.592778432 + 2.85 c = 2.592778432 + 2.85 Combine like terms: 2.592778432 + 2.85 = 5.442778432 c = 5.442778432 Simplifying c = 5.442778432Subproblem 2
c + -2.85 = -2.592778432 Simplifying c + -2.85 = -2.592778432 Reorder the terms: -2.85 + c = -2.592778432 Solving -2.85 + c = -2.592778432 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.85' to each side of the equation. -2.85 + 2.85 + c = -2.592778432 + 2.85 Combine like terms: -2.85 + 2.85 = 0.00 0.00 + c = -2.592778432 + 2.85 c = -2.592778432 + 2.85 Combine like terms: -2.592778432 + 2.85 = 0.257221568 c = 0.257221568 Simplifying c = 0.257221568Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.442778432, 0.257221568}
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