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Simplifying 2c(5c + -1) = 8c + 9 Reorder the terms: 2c(-1 + 5c) = 8c + 9 (-1 * 2c + 5c * 2c) = 8c + 9 (-2c + 10c2) = 8c + 9 Reorder the terms: -2c + 10c2 = 9 + 8c Solving -2c + 10c2 = 9 + 8c Solving for variable 'c'. Reorder the terms: -9 + -2c + -8c + 10c2 = 9 + 8c + -9 + -8c Combine like terms: -2c + -8c = -10c -9 + -10c + 10c2 = 9 + 8c + -9 + -8c Reorder the terms: -9 + -10c + 10c2 = 9 + -9 + 8c + -8c Combine like terms: 9 + -9 = 0 -9 + -10c + 10c2 = 0 + 8c + -8c -9 + -10c + 10c2 = 8c + -8c Combine like terms: 8c + -8c = 0 -9 + -10c + 10c2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + -1c + c2 = 0.0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + -1c + 0.9 + c2 = 0.0 + 0.9 Reorder the terms: -0.9 + 0.9 + -1c + c2 = 0.0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + -1c + c2 = 0.0 + 0.9 -1c + c2 = 0.0 + 0.9 Combine like terms: 0.0 + 0.9 = 0.9 -1c + c2 = 0.9 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 = 0.9 + 0.25 Reorder the terms: 0.25 + -1c + c2 = 0.9 + 0.25 Combine like terms: 0.9 + 0.25 = 1.15 0.25 + -1c + c2 = 1.15 Factor a perfect square on the left side: (c + -0.5)(c + -0.5) = 1.15 Calculate the square root of the right side: 1.072380529 Break this problem into two subproblems by setting (c + -0.5) equal to 1.072380529 and -1.072380529.Subproblem 1
c + -0.5 = 1.072380529 Simplifying c + -0.5 = 1.072380529 Reorder the terms: -0.5 + c = 1.072380529 Solving -0.5 + c = 1.072380529 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 = 1.072380529 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = 1.072380529 + 0.5 c = 1.072380529 + 0.5 Combine like terms: 1.072380529 + 0.5 = 1.572380529 c = 1.572380529 Simplifying c = 1.572380529Subproblem 2
c + -0.5 = -1.072380529 Simplifying c + -0.5 = -1.072380529 Reorder the terms: -0.5 + c = -1.072380529 Solving -0.5 + c = -1.072380529 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 = -1.072380529 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = -1.072380529 + 0.5 c = -1.072380529 + 0.5 Combine like terms: -1.072380529 + 0.5 = -0.572380529 c = -0.572380529 Simplifying c = -0.572380529Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.572380529, -0.572380529}
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