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Simplifying 8c2 + -30c = -9 Reorder the terms: -30c + 8c2 = -9 Solving -30c + 8c2 = -9 Solving for variable 'c'. Reorder the terms: 9 + -30c + 8c2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -30c + 8c2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + -3.75c + c2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -3.75c + -1.125 + c2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -3.75c + c2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -3.75c + c2 = 0 + -1.125 -3.75c + c2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -3.75c + c2 = -1.125 The c term is -3.75c. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75c + 3.515625 + c2 = -1.125 + 3.515625 Reorder the terms: 3.515625 + -3.75c + c2 = -1.125 + 3.515625 Combine like terms: -1.125 + 3.515625 = 2.390625 3.515625 + -3.75c + c2 = 2.390625 Factor a perfect square on the left side: (c + -1.875)(c + -1.875) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (c + -1.875) equal to 1.54616461 and -1.54616461.Subproblem 1
c + -1.875 = 1.54616461 Simplifying c + -1.875 = 1.54616461 Reorder the terms: -1.875 + c = 1.54616461 Solving -1.875 + c = 1.54616461 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + c = 1.54616461 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + c = 1.54616461 + 1.875 c = 1.54616461 + 1.875 Combine like terms: 1.54616461 + 1.875 = 3.42116461 c = 3.42116461 Simplifying c = 3.42116461Subproblem 2
c + -1.875 = -1.54616461 Simplifying c + -1.875 = -1.54616461 Reorder the terms: -1.875 + c = -1.54616461 Solving -1.875 + c = -1.54616461 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + c = -1.54616461 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + c = -1.54616461 + 1.875 c = -1.54616461 + 1.875 Combine like terms: -1.54616461 + 1.875 = 0.32883539 c = 0.32883539 Simplifying c = 0.32883539Solution
The solution to the problem is based on the solutions from the subproblems. c = {3.42116461, 0.32883539}
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