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Simplifying 2c2 + 29c = 14 Reorder the terms: 29c + 2c2 = 14 Solving 29c + 2c2 = 14 Solving for variable 'c'. Reorder the terms: -14 + 29c + 2c2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 29c + 2c2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7 + 14.5c + c2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 14.5c + 7 + c2 = 0 + 7 Reorder the terms: -7 + 7 + 14.5c + c2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 14.5c + c2 = 0 + 7 14.5c + c2 = 0 + 7 Combine like terms: 0 + 7 = 7 14.5c + c2 = 7 The c term is 14.5c. Take half its coefficient (7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. 14.5c + 52.5625 + c2 = 7 + 52.5625 Reorder the terms: 52.5625 + 14.5c + c2 = 7 + 52.5625 Combine like terms: 7 + 52.5625 = 59.5625 52.5625 + 14.5c + c2 = 59.5625 Factor a perfect square on the left side: (c + 7.25)(c + 7.25) = 59.5625 Calculate the square root of the right side: 7.71767452 Break this problem into two subproblems by setting (c + 7.25) equal to 7.71767452 and -7.71767452.Subproblem 1
c + 7.25 = 7.71767452 Simplifying c + 7.25 = 7.71767452 Reorder the terms: 7.25 + c = 7.71767452 Solving 7.25 + c = 7.71767452 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + c = 7.71767452 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + c = 7.71767452 + -7.25 c = 7.71767452 + -7.25 Combine like terms: 7.71767452 + -7.25 = 0.46767452 c = 0.46767452 Simplifying c = 0.46767452Subproblem 2
c + 7.25 = -7.71767452 Simplifying c + 7.25 = -7.71767452 Reorder the terms: 7.25 + c = -7.71767452 Solving 7.25 + c = -7.71767452 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + c = -7.71767452 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + c = -7.71767452 + -7.25 c = -7.71767452 + -7.25 Combine like terms: -7.71767452 + -7.25 = -14.96767452 c = -14.96767452 Simplifying c = -14.96767452Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.46767452, -14.96767452}
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