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Simplifying 3c2 + 18c + 5 = 0 Reorder the terms: 5 + 18c + 3c2 = 0 Solving 5 + 18c + 3c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + 6c + c2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 6c + -1.666666667 + c2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 6c + c2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 6c + c2 = 0 + -1.666666667 6c + c2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 6c + c2 = -1.666666667 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 = -1.666666667 + 9 Reorder the terms: 9 + 6c + c2 = -1.666666667 + 9 Combine like terms: -1.666666667 + 9 = 7.333333333 9 + 6c + c2 = 7.333333333 Factor a perfect square on the left side: (c + 3)(c + 3) = 7.333333333 Calculate the square root of the right side: 2.708012801 Break this problem into two subproblems by setting (c + 3) equal to 2.708012801 and -2.708012801.Subproblem 1
c + 3 = 2.708012801 Simplifying c + 3 = 2.708012801 Reorder the terms: 3 + c = 2.708012801 Solving 3 + c = 2.708012801 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 = 2.708012801 + -3 Combine like terms: 3 + -3 = 0 0 + c = 2.708012801 + -3 c = 2.708012801 + -3 Combine like terms: 2.708012801 + -3 = -0.291987199 c = -0.291987199 Simplifying c = -0.291987199Subproblem 2
c + 3 = -2.708012801 Simplifying c + 3 = -2.708012801 Reorder the terms: 3 + c = -2.708012801 Solving 3 + c = -2.708012801 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 = -2.708012801 + -3 Combine like terms: 3 + -3 = 0 0 + c = -2.708012801 + -3 c = -2.708012801 + -3 Combine like terms: -2.708012801 + -3 = -5.708012801 c = -5.708012801 Simplifying c = -5.708012801Solution
The solution to the problem is based on the solutions from the subproblems. c = {-0.291987199, -5.708012801}
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