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Simplifying 6c2 + -2c + -15 = 0 Reorder the terms: -15 + -2c + 6c2 = 0 Solving -15 + -2c + 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'. -2.5 + -0.3333333333c + c2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -0.3333333333c + 2.5 + c2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -0.3333333333c + c2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -0.3333333333c + c2 = 0 + 2.5 -0.3333333333c + c2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -0.3333333333c + c2 = 2.5 The c term is -0.3333333333c. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333c + 0.02777777779 + c2 = 2.5 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333c + c2 = 2.5 + 0.02777777779 Combine like terms: 2.5 + 0.02777777779 = 2.52777777779 0.02777777779 + -0.3333333333c + c2 = 2.52777777779 Factor a perfect square on the left side: (c + -0.1666666667)(c + -0.1666666667) = 2.52777777779 Calculate the square root of the right side: 1.589898669 Break this problem into two subproblems by setting (c + -0.1666666667) equal to 1.589898669 and -1.589898669.Subproblem 1
c + -0.1666666667 = 1.589898669 Simplifying c + -0.1666666667 = 1.589898669 Reorder the terms: -0.1666666667 + c = 1.589898669 Solving -0.1666666667 + c = 1.589898669 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + c = 1.589898669 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + c = 1.589898669 + 0.1666666667 c = 1.589898669 + 0.1666666667 Combine like terms: 1.589898669 + 0.1666666667 = 1.7565653357 c = 1.7565653357 Simplifying c = 1.7565653357Subproblem 2
c + -0.1666666667 = -1.589898669 Simplifying c + -0.1666666667 = -1.589898669 Reorder the terms: -0.1666666667 + c = -1.589898669 Solving -0.1666666667 + c = -1.589898669 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + c = -1.589898669 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + c = -1.589898669 + 0.1666666667 c = -1.589898669 + 0.1666666667 Combine like terms: -1.589898669 + 0.1666666667 = -1.4232320023 c = -1.4232320023 Simplifying c = -1.4232320023Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.7565653357, -1.4232320023}
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