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Simplifying 9c(c + -4) + 3 = 2 + c + -35 Reorder the terms: 9c(-4 + c) + 3 = 2 + c + -35 (-4 * 9c + c * 9c) + 3 = 2 + c + -35 (-36c + 9c2) + 3 = 2 + c + -35 Reorder the terms: 3 + -36c + 9c2 = 2 + c + -35 Reorder the terms: 3 + -36c + 9c2 = 2 + -35 + c Combine like terms: 2 + -35 = -33 3 + -36c + 9c2 = -33 + c Solving 3 + -36c + 9c2 = -33 + c Solving for variable 'c'. Reorder the terms: 3 + 33 + -36c + -1c + 9c2 = -33 + c + 33 + -1c Combine like terms: 3 + 33 = 36 36 + -36c + -1c + 9c2 = -33 + c + 33 + -1c Combine like terms: -36c + -1c = -37c 36 + -37c + 9c2 = -33 + c + 33 + -1c Reorder the terms: 36 + -37c + 9c2 = -33 + 33 + c + -1c Combine like terms: -33 + 33 = 0 36 + -37c + 9c2 = 0 + c + -1c 36 + -37c + 9c2 = c + -1c Combine like terms: c + -1c = 0 36 + -37c + 9c2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 4 + -4.111111111c + c2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -4.111111111c + -4 + c2 = 0 + -4 Reorder the terms: 4 + -4 + -4.111111111c + c2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4.111111111c + c2 = 0 + -4 -4.111111111c + c2 = 0 + -4 Combine like terms: 0 + -4 = -4 -4.111111111c + c2 = -4 The c term is -4.111111111c. Take half its coefficient (-2.055555556). Square it (4.225308644) and add it to both sides. Add '4.225308644' to each side of the equation. -4.111111111c + 4.225308644 + c2 = -4 + 4.225308644 Reorder the terms: 4.225308644 + -4.111111111c + c2 = -4 + 4.225308644 Combine like terms: -4 + 4.225308644 = 0.225308644 4.225308644 + -4.111111111c + c2 = 0.225308644 Factor a perfect square on the left side: (c + -2.055555556)(c + -2.055555556) = 0.225308644 Calculate the square root of the right side: 0.474666877 Break this problem into two subproblems by setting (c + -2.055555556) equal to 0.474666877 and -0.474666877.Subproblem 1
c + -2.055555556 = 0.474666877 Simplifying c + -2.055555556 = 0.474666877 Reorder the terms: -2.055555556 + c = 0.474666877 Solving -2.055555556 + c = 0.474666877 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.055555556' to each side of the equation. -2.055555556 + 2.055555556 + c = 0.474666877 + 2.055555556 Combine like terms: -2.055555556 + 2.055555556 = 0.000000000 0.000000000 + c = 0.474666877 + 2.055555556 c = 0.474666877 + 2.055555556 Combine like terms: 0.474666877 + 2.055555556 = 2.530222433 c = 2.530222433 Simplifying c = 2.530222433Subproblem 2
c + -2.055555556 = -0.474666877 Simplifying c + -2.055555556 = -0.474666877 Reorder the terms: -2.055555556 + c = -0.474666877 Solving -2.055555556 + c = -0.474666877 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.055555556' to each side of the equation. -2.055555556 + 2.055555556 + c = -0.474666877 + 2.055555556 Combine like terms: -2.055555556 + 2.055555556 = 0.000000000 0.000000000 + c = -0.474666877 + 2.055555556 c = -0.474666877 + 2.055555556 Combine like terms: -0.474666877 + 2.055555556 = 1.580888679 c = 1.580888679 Simplifying c = 1.580888679Solution
The solution to the problem is based on the solutions from the subproblems. c = {2.530222433, 1.580888679}
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