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Simplifying c2 + 6c + -9 = 0 Reorder the terms: -9 + 6c + c2 = 0 Solving -9 + 6c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 6c + 9 + c2 = 0 + 9 Reorder the terms: -9 + 9 + 6c + c2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 6c + c2 = 0 + 9 6c + c2 = 0 + 9 Combine like terms: 0 + 9 = 9 6c + c2 = 9 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 = 9 + 9 Reorder the terms: 9 + 6c + c2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + 6c + c2 = 18 Factor a perfect square on the left side: (c + 3)(c + 3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (c + 3) equal to 4.242640687 and -4.242640687.Subproblem 1
c + 3 = 4.242640687 Simplifying c + 3 = 4.242640687 Reorder the terms: 3 + c = 4.242640687 Solving 3 + c = 4.242640687 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 = 4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + c = 4.242640687 + -3 c = 4.242640687 + -3 Combine like terms: 4.242640687 + -3 = 1.242640687 c = 1.242640687 Simplifying c = 1.242640687Subproblem 2
c + 3 = -4.242640687 Simplifying c + 3 = -4.242640687 Reorder the terms: 3 + c = -4.242640687 Solving 3 + c = -4.242640687 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 = -4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + c = -4.242640687 + -3 c = -4.242640687 + -3 Combine like terms: -4.242640687 + -3 = -7.242640687 c = -7.242640687 Simplifying c = -7.242640687Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.242640687, -7.242640687}
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