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Simplifying 9c + c * 2c + -3 = 9 Reorder the terms for easier multiplication: 9c + 2c * c + -3 = 9 Multiply c * c 9c + 2c2 + -3 = 9 Reorder the terms: -3 + 9c + 2c2 = 9 Solving -3 + 9c + 2c2 = 9 Solving for variable 'c'. Reorder the terms: -3 + -9 + 9c + 2c2 = 9 + -9 Combine like terms: -3 + -9 = -12 -12 + 9c + 2c2 = 9 + -9 Combine like terms: 9 + -9 = 0 -12 + 9c + 2c2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + 4.5c + c2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 4.5c + 6 + c2 = 0 + 6 Reorder the terms: -6 + 6 + 4.5c + c2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 4.5c + c2 = 0 + 6 4.5c + c2 = 0 + 6 Combine like terms: 0 + 6 = 6 4.5c + c2 = 6 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 = 6 + 5.0625 Reorder the terms: 5.0625 + 4.5c + c2 = 6 + 5.0625 Combine like terms: 6 + 5.0625 = 11.0625 5.0625 + 4.5c + c2 = 11.0625 Factor a perfect square on the left side: (c + 2.25)(c + 2.25) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (c + 2.25) equal to 3.326033674 and -3.326033674.Subproblem 1
c + 2.25 = 3.326033674 Simplifying c + 2.25 = 3.326033674 Reorder the terms: 2.25 + c = 3.326033674 Solving 2.25 + c = 3.326033674 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 = 3.326033674 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + c = 3.326033674 + -2.25 c = 3.326033674 + -2.25 Combine like terms: 3.326033674 + -2.25 = 1.076033674 c = 1.076033674 Simplifying c = 1.076033674Subproblem 2
c + 2.25 = -3.326033674 Simplifying c + 2.25 = -3.326033674 Reorder the terms: 2.25 + c = -3.326033674 Solving 2.25 + c = -3.326033674 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 = -3.326033674 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + c = -3.326033674 + -2.25 c = -3.326033674 + -2.25 Combine like terms: -3.326033674 + -2.25 = -5.576033674 c = -5.576033674 Simplifying c = -5.576033674Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.076033674, -5.576033674}
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