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Simplifying 6c2 + -34c + 9 = 0 Reorder the terms: 9 + -34c + 6c2 = 0 Solving 9 + -34c + 6c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.5 + -5.666666667c + c2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -5.666666667c + -1.5 + c2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -5.666666667c + c2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -5.666666667c + c2 = 0 + -1.5 -5.666666667c + c2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -5.666666667c + c2 = -1.5 The c term is -5.666666667c. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667c + 8.027777782 + c2 = -1.5 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667c + c2 = -1.5 + 8.027777782 Combine like terms: -1.5 + 8.027777782 = 6.527777782 8.027777782 + -5.666666667c + c2 = 6.527777782 Factor a perfect square on the left side: (c + -2.833333334)(c + -2.833333334) = 6.527777782 Calculate the square root of the right side: 2.55495162 Break this problem into two subproblems by setting (c + -2.833333334) equal to 2.55495162 and -2.55495162.Subproblem 1
c + -2.833333334 = 2.55495162 Simplifying c + -2.833333334 = 2.55495162 Reorder the terms: -2.833333334 + c = 2.55495162 Solving -2.833333334 + c = 2.55495162 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + c = 2.55495162 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + c = 2.55495162 + 2.833333334 c = 2.55495162 + 2.833333334 Combine like terms: 2.55495162 + 2.833333334 = 5.388284954 c = 5.388284954 Simplifying c = 5.388284954Subproblem 2
c + -2.833333334 = -2.55495162 Simplifying c + -2.833333334 = -2.55495162 Reorder the terms: -2.833333334 + c = -2.55495162 Solving -2.833333334 + c = -2.55495162 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + c = -2.55495162 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + c = -2.55495162 + 2.833333334 c = -2.55495162 + 2.833333334 Combine like terms: -2.55495162 + 2.833333334 = 0.278381714 c = 0.278381714 Simplifying c = 0.278381714Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.388284954, 0.278381714}
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