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Simplifying 5c2 + -36c + -24 = 0 Reorder the terms: -24 + -36c + 5c2 = 0 Solving -24 + -36c + 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'. -4.8 + -7.2c + c2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -7.2c + 4.8 + c2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -7.2c + c2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -7.2c + c2 = 0 + 4.8 -7.2c + c2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -7.2c + c2 = 4.8 The c term is -7.2c. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2c + 12.96 + c2 = 4.8 + 12.96 Reorder the terms: 12.96 + -7.2c + c2 = 4.8 + 12.96 Combine like terms: 4.8 + 12.96 = 17.76 12.96 + -7.2c + c2 = 17.76 Factor a perfect square on the left side: (c + -3.6)(c + -3.6) = 17.76 Calculate the square root of the right side: 4.214261501 Break this problem into two subproblems by setting (c + -3.6) equal to 4.214261501 and -4.214261501.Subproblem 1
c + -3.6 = 4.214261501 Simplifying c + -3.6 = 4.214261501 Reorder the terms: -3.6 + c = 4.214261501 Solving -3.6 + c = 4.214261501 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + c = 4.214261501 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + c = 4.214261501 + 3.6 c = 4.214261501 + 3.6 Combine like terms: 4.214261501 + 3.6 = 7.814261501 c = 7.814261501 Simplifying c = 7.814261501Subproblem 2
c + -3.6 = -4.214261501 Simplifying c + -3.6 = -4.214261501 Reorder the terms: -3.6 + c = -4.214261501 Solving -3.6 + c = -4.214261501 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + c = -4.214261501 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + c = -4.214261501 + 3.6 c = -4.214261501 + 3.6 Combine like terms: -4.214261501 + 3.6 = -0.614261501 c = -0.614261501 Simplifying c = -0.614261501Solution
The solution to the problem is based on the solutions from the subproblems. c = {7.814261501, -0.614261501}
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