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Simplifying 16 + -1c2 = 4c + 2 Reorder the terms: 16 + -1c2 = 2 + 4c Solving 16 + -1c2 = 2 + 4c Solving for variable 'c'. Reorder the terms: 16 + -2 + -4c + -1c2 = 2 + 4c + -2 + -4c Combine like terms: 16 + -2 = 14 14 + -4c + -1c2 = 2 + 4c + -2 + -4c Reorder the terms: 14 + -4c + -1c2 = 2 + -2 + 4c + -4c Combine like terms: 2 + -2 = 0 14 + -4c + -1c2 = 0 + 4c + -4c 14 + -4c + -1c2 = 4c + -4c Combine like terms: 4c + -4c = 0 14 + -4c + -1c2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + 4c + c2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 4c + 14 + c2 = 0 + 14 Reorder the terms: -14 + 14 + 4c + c2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 4c + c2 = 0 + 14 4c + c2 = 0 + 14 Combine like terms: 0 + 14 = 14 4c + c2 = 14 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 = 14 + 4 Reorder the terms: 4 + 4c + c2 = 14 + 4 Combine like terms: 14 + 4 = 18 4 + 4c + c2 = 18 Factor a perfect square on the left side: (c + 2)(c + 2) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (c + 2) equal to 4.242640687 and -4.242640687.Subproblem 1
c + 2 = 4.242640687 Simplifying c + 2 = 4.242640687 Reorder the terms: 2 + c = 4.242640687 Solving 2 + c = 4.242640687 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 = 4.242640687 + -2 Combine like terms: 2 + -2 = 0 0 + c = 4.242640687 + -2 c = 4.242640687 + -2 Combine like terms: 4.242640687 + -2 = 2.242640687 c = 2.242640687 Simplifying c = 2.242640687Subproblem 2
c + 2 = -4.242640687 Simplifying c + 2 = -4.242640687 Reorder the terms: 2 + c = -4.242640687 Solving 2 + c = -4.242640687 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 = -4.242640687 + -2 Combine like terms: 2 + -2 = 0 0 + c = -4.242640687 + -2 c = -4.242640687 + -2 Combine like terms: -4.242640687 + -2 = -6.242640687 c = -6.242640687 Simplifying c = -6.242640687Solution
The solution to the problem is based on the solutions from the subproblems. c = {2.242640687, -6.242640687}
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