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Simplifying 29 + -1c(2c + 4) = 2(c + 5) + c Reorder the terms: 29 + -1c(4 + 2c) = 2(c + 5) + c 29 + (4 * -1c + 2c * -1c) = 2(c + 5) + c 29 + (-4c + -2c2) = 2(c + 5) + c Reorder the terms: 29 + -4c + -2c2 = 2(5 + c) + c 29 + -4c + -2c2 = (5 * 2 + c * 2) + c 29 + -4c + -2c2 = (10 + 2c) + c Combine like terms: 2c + c = 3c 29 + -4c + -2c2 = 10 + 3c Solving 29 + -4c + -2c2 = 10 + 3c Solving for variable 'c'. Reorder the terms: 29 + -10 + -4c + -3c + -2c2 = 10 + 3c + -10 + -3c Combine like terms: 29 + -10 = 19 19 + -4c + -3c + -2c2 = 10 + 3c + -10 + -3c Combine like terms: -4c + -3c = -7c 19 + -7c + -2c2 = 10 + 3c + -10 + -3c Reorder the terms: 19 + -7c + -2c2 = 10 + -10 + 3c + -3c Combine like terms: 10 + -10 = 0 19 + -7c + -2c2 = 0 + 3c + -3c 19 + -7c + -2c2 = 3c + -3c Combine like terms: 3c + -3c = 0 19 + -7c + -2c2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -9.5 + 3.5c + c2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 3.5c + 9.5 + c2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 3.5c + c2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 3.5c + c2 = 0 + 9.5 3.5c + c2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 3.5c + c2 = 9.5 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 = 9.5 + 3.0625 Reorder the terms: 3.0625 + 3.5c + c2 = 9.5 + 3.0625 Combine like terms: 9.5 + 3.0625 = 12.5625 3.0625 + 3.5c + c2 = 12.5625 Factor a perfect square on the left side: (c + 1.75)(c + 1.75) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (c + 1.75) equal to 3.54436172 and -3.54436172.Subproblem 1
c + 1.75 = 3.54436172 Simplifying c + 1.75 = 3.54436172 Reorder the terms: 1.75 + c = 3.54436172 Solving 1.75 + c = 3.54436172 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 = 3.54436172 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + c = 3.54436172 + -1.75 c = 3.54436172 + -1.75 Combine like terms: 3.54436172 + -1.75 = 1.79436172 c = 1.79436172 Simplifying c = 1.79436172Subproblem 2
c + 1.75 = -3.54436172 Simplifying c + 1.75 = -3.54436172 Reorder the terms: 1.75 + c = -3.54436172 Solving 1.75 + c = -3.54436172 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 = -3.54436172 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + c = -3.54436172 + -1.75 c = -3.54436172 + -1.75 Combine like terms: -3.54436172 + -1.75 = -5.29436172 c = -5.29436172 Simplifying c = -5.29436172Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.79436172, -5.29436172}
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