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Simplifying 48c2 + 19c + -21 = 0 Reorder the terms: -21 + 19c + 48c2 = 0 Solving -21 + 19c + 48c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.4375 + 0.3958333333c + c2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + 0.3958333333c + 0.4375 + c2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + 0.3958333333c + c2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + 0.3958333333c + c2 = 0 + 0.4375 0.3958333333c + c2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 0.3958333333c + c2 = 0.4375 The c term is 0.3958333333c. Take half its coefficient (0.1979166667). Square it (0.03917100696) and add it to both sides. Add '0.03917100696' to each side of the equation. 0.3958333333c + 0.03917100696 + c2 = 0.4375 + 0.03917100696 Reorder the terms: 0.03917100696 + 0.3958333333c + c2 = 0.4375 + 0.03917100696 Combine like terms: 0.4375 + 0.03917100696 = 0.47667100696 0.03917100696 + 0.3958333333c + c2 = 0.47667100696 Factor a perfect square on the left side: (c + 0.1979166667)(c + 0.1979166667) = 0.47667100696 Calculate the square root of the right side: 0.690413649 Break this problem into two subproblems by setting (c + 0.1979166667) equal to 0.690413649 and -0.690413649.Subproblem 1
c + 0.1979166667 = 0.690413649 Simplifying c + 0.1979166667 = 0.690413649 Reorder the terms: 0.1979166667 + c = 0.690413649 Solving 0.1979166667 + c = 0.690413649 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.1979166667' to each side of the equation. 0.1979166667 + -0.1979166667 + c = 0.690413649 + -0.1979166667 Combine like terms: 0.1979166667 + -0.1979166667 = 0.0000000000 0.0000000000 + c = 0.690413649 + -0.1979166667 c = 0.690413649 + -0.1979166667 Combine like terms: 0.690413649 + -0.1979166667 = 0.4924969823 c = 0.4924969823 Simplifying c = 0.4924969823Subproblem 2
c + 0.1979166667 = -0.690413649 Simplifying c + 0.1979166667 = -0.690413649 Reorder the terms: 0.1979166667 + c = -0.690413649 Solving 0.1979166667 + c = -0.690413649 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.1979166667' to each side of the equation. 0.1979166667 + -0.1979166667 + c = -0.690413649 + -0.1979166667 Combine like terms: 0.1979166667 + -0.1979166667 = 0.0000000000 0.0000000000 + c = -0.690413649 + -0.1979166667 c = -0.690413649 + -0.1979166667 Combine like terms: -0.690413649 + -0.1979166667 = -0.8883303157 c = -0.8883303157 Simplifying c = -0.8883303157Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.4924969823, -0.8883303157}
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