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Simplifying 5c2 + -13c + -48 = 0 Reorder the terms: -48 + -13c + 5c2 = 0 Solving -48 + -13c + 5c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.6 + -2.6c + c2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + -2.6c + 9.6 + c2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + -2.6c + c2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + -2.6c + c2 = 0 + 9.6 -2.6c + c2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 -2.6c + c2 = 9.6 The c term is -2.6c. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6c + 1.69 + c2 = 9.6 + 1.69 Reorder the terms: 1.69 + -2.6c + c2 = 9.6 + 1.69 Combine like terms: 9.6 + 1.69 = 11.29 1.69 + -2.6c + c2 = 11.29 Factor a perfect square on the left side: (c + -1.3)(c + -1.3) = 11.29 Calculate the square root of the right side: 3.360059523 Break this problem into two subproblems by setting (c + -1.3) equal to 3.360059523 and -3.360059523.Subproblem 1
c + -1.3 = 3.360059523 Simplifying c + -1.3 = 3.360059523 Reorder the terms: -1.3 + c = 3.360059523 Solving -1.3 + c = 3.360059523 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + c = 3.360059523 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + c = 3.360059523 + 1.3 c = 3.360059523 + 1.3 Combine like terms: 3.360059523 + 1.3 = 4.660059523 c = 4.660059523 Simplifying c = 4.660059523Subproblem 2
c + -1.3 = -3.360059523 Simplifying c + -1.3 = -3.360059523 Reorder the terms: -1.3 + c = -3.360059523 Solving -1.3 + c = -3.360059523 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + c = -3.360059523 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + c = -3.360059523 + 1.3 c = -3.360059523 + 1.3 Combine like terms: -3.360059523 + 1.3 = -2.060059523 c = -2.060059523 Simplifying c = -2.060059523Solution
The solution to the problem is based on the solutions from the subproblems. c = {4.660059523, -2.060059523}
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