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Simplifying c2 + -6c + 9 = 3 Reorder the terms: 9 + -6c + c2 = 3 Solving 9 + -6c + c2 = 3 Solving for variable 'c'. Reorder the terms: 9 + -3 + -6c + c2 = 3 + -3 Combine like terms: 9 + -3 = 6 6 + -6c + c2 = 3 + -3 Combine like terms: 3 + -3 = 0 6 + -6c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -6c + -6 + c2 = 0 + -6 Reorder the terms: 6 + -6 + -6c + c2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -6c + c2 = 0 + -6 -6c + c2 = 0 + -6 Combine like terms: 0 + -6 = -6 -6c + c2 = -6 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 = -6 + 9 Reorder the terms: 9 + -6c + c2 = -6 + 9 Combine like terms: -6 + 9 = 3 9 + -6c + c2 = 3 Factor a perfect square on the left side: (c + -3)(c + -3) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (c + -3) equal to 1.732050808 and -1.732050808.Subproblem 1
c + -3 = 1.732050808 Simplifying c + -3 = 1.732050808 Reorder the terms: -3 + c = 1.732050808 Solving -3 + c = 1.732050808 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 = 1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + c = 1.732050808 + 3 c = 1.732050808 + 3 Combine like terms: 1.732050808 + 3 = 4.732050808 c = 4.732050808 Simplifying c = 4.732050808Subproblem 2
c + -3 = -1.732050808 Simplifying c + -3 = -1.732050808 Reorder the terms: -3 + c = -1.732050808 Solving -3 + c = -1.732050808 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 = -1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + c = -1.732050808 + 3 c = -1.732050808 + 3 Combine like terms: -1.732050808 + 3 = 1.267949192 c = 1.267949192 Simplifying c = 1.267949192Solution
The solution to the problem is based on the solutions from the subproblems. c = {4.732050808, 1.267949192}
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