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Simplifying 5(c + -4) * c = 9 Reorder the terms: 5(-4 + c) * c = 9 Reorder the terms for easier multiplication: 5c(-4 + c) = 9 (-4 * 5c + c * 5c) = 9 (-20c + 5c2) = 9 Solving -20c + 5c2 = 9 Solving for variable 'c'. Reorder the terms: -9 + -20c + 5c2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -20c + 5c2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + -4c + c2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -4c + 1.8 + c2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -4c + c2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -4c + c2 = 0 + 1.8 -4c + c2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -4c + c2 = 1.8 The c term is -4c. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4c + 4 + c2 = 1.8 + 4 Reorder the terms: 4 + -4c + c2 = 1.8 + 4 Combine like terms: 1.8 + 4 = 5.8 4 + -4c + c2 = 5.8 Factor a perfect square on the left side: (c + -2)(c + -2) = 5.8 Calculate the square root of the right side: 2.408318916 Break this problem into two subproblems by setting (c + -2) equal to 2.408318916 and -2.408318916.Subproblem 1
c + -2 = 2.408318916 Simplifying c + -2 = 2.408318916 Reorder the terms: -2 + c = 2.408318916 Solving -2 + c = 2.408318916 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c = 2.408318916 + 2 Combine like terms: -2 + 2 = 0 0 + c = 2.408318916 + 2 c = 2.408318916 + 2 Combine like terms: 2.408318916 + 2 = 4.408318916 c = 4.408318916 Simplifying c = 4.408318916Subproblem 2
c + -2 = -2.408318916 Simplifying c + -2 = -2.408318916 Reorder the terms: -2 + c = -2.408318916 Solving -2 + c = -2.408318916 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c = -2.408318916 + 2 Combine like terms: -2 + 2 = 0 0 + c = -2.408318916 + 2 c = -2.408318916 + 2 Combine like terms: -2.408318916 + 2 = -0.408318916 c = -0.408318916 Simplifying c = -0.408318916Solution
The solution to the problem is based on the solutions from the subproblems. c = {4.408318916, -0.408318916}
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