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Simplifying c2 + -8c + -2 = 0 Reorder the terms: -2 + -8c + c2 = 0 Solving -2 + -8c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -8c + 2 + c2 = 0 + 2 Reorder the terms: -2 + 2 + -8c + c2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -8c + c2 = 0 + 2 -8c + c2 = 0 + 2 Combine like terms: 0 + 2 = 2 -8c + c2 = 2 The c term is -8c. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8c + 16 + c2 = 2 + 16 Reorder the terms: 16 + -8c + c2 = 2 + 16 Combine like terms: 2 + 16 = 18 16 + -8c + c2 = 18 Factor a perfect square on the left side: (c + -4)(c + -4) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (c + -4) equal to 4.242640687 and -4.242640687.Subproblem 1
c + -4 = 4.242640687 Simplifying c + -4 = 4.242640687 Reorder the terms: -4 + c = 4.242640687 Solving -4 + c = 4.242640687 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + c = 4.242640687 + 4 Combine like terms: -4 + 4 = 0 0 + c = 4.242640687 + 4 c = 4.242640687 + 4 Combine like terms: 4.242640687 + 4 = 8.242640687 c = 8.242640687 Simplifying c = 8.242640687Subproblem 2
c + -4 = -4.242640687 Simplifying c + -4 = -4.242640687 Reorder the terms: -4 + c = -4.242640687 Solving -4 + c = -4.242640687 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + c = -4.242640687 + 4 Combine like terms: -4 + 4 = 0 0 + c = -4.242640687 + 4 c = -4.242640687 + 4 Combine like terms: -4.242640687 + 4 = -0.242640687 c = -0.242640687 Simplifying c = -0.242640687Solution
The solution to the problem is based on the solutions from the subproblems. c = {8.242640687, -0.242640687}
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