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Simplifying 9(c + -1) * c = 2 Reorder the terms: 9(-1 + c) * c = 2 Reorder the terms for easier multiplication: 9c(-1 + c) = 2 (-1 * 9c + c * 9c) = 2 (-9c + 9c2) = 2 Solving -9c + 9c2 = 2 Solving for variable 'c'. Reorder the terms: -2 + -9c + 9c2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -9c + 9c2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.2222222222 + -1c + c2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -1c + 0.2222222222 + c2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -1c + c2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -1c + c2 = 0 + 0.2222222222 -1c + c2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -1c + c2 = 0.2222222222 The c term is -1c. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1c + 0.25 + c2 = 0.2222222222 + 0.25 Reorder the terms: 0.25 + -1c + c2 = 0.2222222222 + 0.25 Combine like terms: 0.2222222222 + 0.25 = 0.4722222222 0.25 + -1c + c2 = 0.4722222222 Factor a perfect square on the left side: (c + -0.5)(c + -0.5) = 0.4722222222 Calculate the square root of the right side: 0.687184271 Break this problem into two subproblems by setting (c + -0.5) equal to 0.687184271 and -0.687184271.Subproblem 1
c + -0.5 = 0.687184271 Simplifying c + -0.5 = 0.687184271 Reorder the terms: -0.5 + c = 0.687184271 Solving -0.5 + c = 0.687184271 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + c = 0.687184271 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = 0.687184271 + 0.5 c = 0.687184271 + 0.5 Combine like terms: 0.687184271 + 0.5 = 1.187184271 c = 1.187184271 Simplifying c = 1.187184271Subproblem 2
c + -0.5 = -0.687184271 Simplifying c + -0.5 = -0.687184271 Reorder the terms: -0.5 + c = -0.687184271 Solving -0.5 + c = -0.687184271 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + c = -0.687184271 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = -0.687184271 + 0.5 c = -0.687184271 + 0.5 Combine like terms: -0.687184271 + 0.5 = -0.187184271 c = -0.187184271 Simplifying c = -0.187184271Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.187184271, -0.187184271}
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