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Simplifying c(2c + 11) = 10 Reorder the terms: c(11 + 2c) = 10 (11 * c + 2c * c) = 10 (11c + 2c2) = 10 Solving 11c + 2c2 = 10 Solving for variable 'c'. Reorder the terms: -10 + 11c + 2c2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 11c + 2c2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + 5.5c + c2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 5.5c + 5 + c2 = 0 + 5 Reorder the terms: -5 + 5 + 5.5c + c2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 5.5c + c2 = 0 + 5 5.5c + c2 = 0 + 5 Combine like terms: 0 + 5 = 5 5.5c + c2 = 5 The c term is 5.5c. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5c + 7.5625 + c2 = 5 + 7.5625 Reorder the terms: 7.5625 + 5.5c + c2 = 5 + 7.5625 Combine like terms: 5 + 7.5625 = 12.5625 7.5625 + 5.5c + c2 = 12.5625 Factor a perfect square on the left side: (c + 2.75)(c + 2.75) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (c + 2.75) equal to 3.54436172 and -3.54436172.Subproblem 1
c + 2.75 = 3.54436172 Simplifying c + 2.75 = 3.54436172 Reorder the terms: 2.75 + c = 3.54436172 Solving 2.75 + c = 3.54436172 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + c = 3.54436172 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + c = 3.54436172 + -2.75 c = 3.54436172 + -2.75 Combine like terms: 3.54436172 + -2.75 = 0.79436172 c = 0.79436172 Simplifying c = 0.79436172Subproblem 2
c + 2.75 = -3.54436172 Simplifying c + 2.75 = -3.54436172 Reorder the terms: 2.75 + c = -3.54436172 Solving 2.75 + c = -3.54436172 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + c = -3.54436172 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + c = -3.54436172 + -2.75 c = -3.54436172 + -2.75 Combine like terms: -3.54436172 + -2.75 = -6.29436172 c = -6.29436172 Simplifying c = -6.29436172Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.79436172, -6.29436172}
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