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Simplifying 9 = c2 + -6c Reorder the terms: 9 = -6c + c2 Solving 9 = -6c + c2 Solving for variable 'c'. Reorder the terms: 9 + 6c + -1c2 = -6c + 6c + c2 + -1c2 Combine like terms: -6c + 6c = 0 9 + 6c + -1c2 = 0 + c2 + -1c2 9 + 6c + -1c2 = c2 + -1c2 Combine like terms: c2 + -1c2 = 0 9 + 6c + -1c2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + -6c + c2 = 0 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 = 7.242640687 c = 7.242640687 Simplifying c = 7.242640687Subproblem 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 = -1.242640687 c = -1.242640687 Simplifying c = -1.242640687Solution
The solution to the problem is based on the solutions from the subproblems. c = {7.242640687, -1.242640687}
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