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Simplifying 2c2 + 9 + 6 = 9c + 14 Reorder the terms: 9 + 6 + 2c2 = 9c + 14 Combine like terms: 9 + 6 = 15 15 + 2c2 = 9c + 14 Reorder the terms: 15 + 2c2 = 14 + 9c Solving 15 + 2c2 = 14 + 9c Solving for variable 'c'. Reorder the terms: 15 + -14 + -9c + 2c2 = 14 + 9c + -14 + -9c Combine like terms: 15 + -14 = 1 1 + -9c + 2c2 = 14 + 9c + -14 + -9c Reorder the terms: 1 + -9c + 2c2 = 14 + -14 + 9c + -9c Combine like terms: 14 + -14 = 0 1 + -9c + 2c2 = 0 + 9c + -9c 1 + -9c + 2c2 = 9c + -9c Combine like terms: 9c + -9c = 0 1 + -9c + 2c2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -4.5c + c2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -4.5c + -0.5 + c2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -4.5c + c2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -4.5c + c2 = 0 + -0.5 -4.5c + c2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -4.5c + c2 = -0.5 The c term is -4.5c. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5c + 5.0625 + c2 = -0.5 + 5.0625 Reorder the terms: 5.0625 + -4.5c + c2 = -0.5 + 5.0625 Combine like terms: -0.5 + 5.0625 = 4.5625 5.0625 + -4.5c + c2 = 4.5625 Factor a perfect square on the left side: (c + -2.25)(c + -2.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (c + -2.25) equal to 2.136000936 and -2.136000936.Subproblem 1
c + -2.25 = 2.136000936 Simplifying c + -2.25 = 2.136000936 Reorder the terms: -2.25 + c = 2.136000936 Solving -2.25 + c = 2.136000936 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + c = 2.136000936 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + c = 2.136000936 + 2.25 c = 2.136000936 + 2.25 Combine like terms: 2.136000936 + 2.25 = 4.386000936 c = 4.386000936 Simplifying c = 4.386000936Subproblem 2
c + -2.25 = -2.136000936 Simplifying c + -2.25 = -2.136000936 Reorder the terms: -2.25 + c = -2.136000936 Solving -2.25 + c = -2.136000936 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + c = -2.136000936 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + c = -2.136000936 + 2.25 c = -2.136000936 + 2.25 Combine like terms: -2.136000936 + 2.25 = 0.113999064 c = 0.113999064 Simplifying c = 0.113999064Solution
The solution to the problem is based on the solutions from the subproblems. c = {4.386000936, 0.113999064}
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