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Simplifying c2 + -4c + -8 = 0 Reorder the terms: -8 + -4c + c2 = 0 Solving -8 + -4c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -4c + 8 + c2 = 0 + 8 Reorder the terms: -8 + 8 + -4c + c2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -4c + c2 = 0 + 8 -4c + c2 = 0 + 8 Combine like terms: 0 + 8 = 8 -4c + c2 = 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 = 8 + 4 Reorder the terms: 4 + -4c + c2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + -4c + c2 = 12 Factor a perfect square on the left side: (c + -2)(c + -2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (c + -2) equal to 3.464101615 and -3.464101615.Subproblem 1
c + -2 = 3.464101615 Simplifying c + -2 = 3.464101615 Reorder the terms: -2 + c = 3.464101615 Solving -2 + c = 3.464101615 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 = 3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + c = 3.464101615 + 2 c = 3.464101615 + 2 Combine like terms: 3.464101615 + 2 = 5.464101615 c = 5.464101615 Simplifying c = 5.464101615Subproblem 2
c + -2 = -3.464101615 Simplifying c + -2 = -3.464101615 Reorder the terms: -2 + c = -3.464101615 Solving -2 + c = -3.464101615 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 = -3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + c = -3.464101615 + 2 c = -3.464101615 + 2 Combine like terms: -3.464101615 + 2 = -1.464101615 c = -1.464101615 Simplifying c = -1.464101615Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.464101615, -1.464101615}
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