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Simplifying -1c2 + -6c + 8 = 0 Reorder the terms: 8 + -6c + -1c2 = 0 Solving 8 + -6c + -1c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + 6c + c2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 6c + 8 + c2 = 0 + 8 Reorder the terms: -8 + 8 + 6c + c2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 6c + c2 = 0 + 8 6c + c2 = 0 + 8 Combine like terms: 0 + 8 = 8 6c + c2 = 8 The c term is 6c. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6c + 9 + c2 = 8 + 9 Reorder the terms: 9 + 6c + c2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + 6c + c2 = 17 Factor a perfect square on the left side: (c + 3)(c + 3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (c + 3) equal to 4.123105626 and -4.123105626.Subproblem 1
c + 3 = 4.123105626 Simplifying c + 3 = 4.123105626 Reorder the terms: 3 + c = 4.123105626 Solving 3 + c = 4.123105626 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + c = 4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + c = 4.123105626 + -3 c = 4.123105626 + -3 Combine like terms: 4.123105626 + -3 = 1.123105626 c = 1.123105626 Simplifying c = 1.123105626Subproblem 2
c + 3 = -4.123105626 Simplifying c + 3 = -4.123105626 Reorder the terms: 3 + c = -4.123105626 Solving 3 + c = -4.123105626 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + c = -4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + c = -4.123105626 + -3 c = -4.123105626 + -3 Combine like terms: -4.123105626 + -3 = -7.123105626 c = -7.123105626 Simplifying c = -7.123105626Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.123105626, -7.123105626}
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