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Simplifying 4c + 3 = 3c(c + -4) Reorder the terms: 3 + 4c = 3c(c + -4) Reorder the terms: 3 + 4c = 3c(-4 + c) 3 + 4c = (-4 * 3c + c * 3c) 3 + 4c = (-12c + 3c2) Solving 3 + 4c = -12c + 3c2 Solving for variable 'c'. Combine like terms: 4c + 12c = 16c 3 + 16c + -3c2 = -12c + 3c2 + 12c + -3c2 Reorder the terms: 3 + 16c + -3c2 = -12c + 12c + 3c2 + -3c2 Combine like terms: -12c + 12c = 0 3 + 16c + -3c2 = 0 + 3c2 + -3c2 3 + 16c + -3c2 = 3c2 + -3c2 Combine like terms: 3c2 + -3c2 = 0 3 + 16c + -3c2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1 + -5.333333333c + c2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -5.333333333c + 1 + c2 = 0 + 1 Reorder the terms: -1 + 1 + -5.333333333c + c2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5.333333333c + c2 = 0 + 1 -5.333333333c + c2 = 0 + 1 Combine like terms: 0 + 1 = 1 -5.333333333c + c2 = 1 The c term is -5.333333333c. Take half its coefficient (-2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. -5.333333333c + 7.111111113 + c2 = 1 + 7.111111113 Reorder the terms: 7.111111113 + -5.333333333c + c2 = 1 + 7.111111113 Combine like terms: 1 + 7.111111113 = 8.111111113 7.111111113 + -5.333333333c + c2 = 8.111111113 Factor a perfect square on the left side: (c + -2.666666667)(c + -2.666666667) = 8.111111113 Calculate the square root of the right side: 2.848001249 Break this problem into two subproblems by setting (c + -2.666666667) equal to 2.848001249 and -2.848001249.Subproblem 1
c + -2.666666667 = 2.848001249 Simplifying c + -2.666666667 = 2.848001249 Reorder the terms: -2.666666667 + c = 2.848001249 Solving -2.666666667 + c = 2.848001249 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + c = 2.848001249 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + c = 2.848001249 + 2.666666667 c = 2.848001249 + 2.666666667 Combine like terms: 2.848001249 + 2.666666667 = 5.514667916 c = 5.514667916 Simplifying c = 5.514667916Subproblem 2
c + -2.666666667 = -2.848001249 Simplifying c + -2.666666667 = -2.848001249 Reorder the terms: -2.666666667 + c = -2.848001249 Solving -2.666666667 + c = -2.848001249 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + c = -2.848001249 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + c = -2.848001249 + 2.666666667 c = -2.848001249 + 2.666666667 Combine like terms: -2.848001249 + 2.666666667 = -0.181334582 c = -0.181334582 Simplifying c = -0.181334582Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.514667916, -0.181334582}
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