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Simplifying 3c2 + -6c + -16 = 0 Reorder the terms: -16 + -6c + 3c2 = 0 Solving -16 + -6c + 3c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + -2c + c2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -2c + 5.333333333 + c2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -2c + c2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -2c + c2 = 0 + 5.333333333 -2c + c2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -2c + c2 = 5.333333333 The c term is -2c. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2c + 1 + c2 = 5.333333333 + 1 Reorder the terms: 1 + -2c + c2 = 5.333333333 + 1 Combine like terms: 5.333333333 + 1 = 6.333333333 1 + -2c + c2 = 6.333333333 Factor a perfect square on the left side: (c + -1)(c + -1) = 6.333333333 Calculate the square root of the right side: 2.516611478 Break this problem into two subproblems by setting (c + -1) equal to 2.516611478 and -2.516611478.Subproblem 1
c + -1 = 2.516611478 Simplifying c + -1 = 2.516611478 Reorder the terms: -1 + c = 2.516611478 Solving -1 + c = 2.516611478 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + c = 2.516611478 + 1 Combine like terms: -1 + 1 = 0 0 + c = 2.516611478 + 1 c = 2.516611478 + 1 Combine like terms: 2.516611478 + 1 = 3.516611478 c = 3.516611478 Simplifying c = 3.516611478Subproblem 2
c + -1 = -2.516611478 Simplifying c + -1 = -2.516611478 Reorder the terms: -1 + c = -2.516611478 Solving -1 + c = -2.516611478 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + c = -2.516611478 + 1 Combine like terms: -1 + 1 = 0 0 + c = -2.516611478 + 1 c = -2.516611478 + 1 Combine like terms: -2.516611478 + 1 = -1.516611478 c = -1.516611478 Simplifying c = -1.516611478Solution
The solution to the problem is based on the solutions from the subproblems. c = {3.516611478, -1.516611478}
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