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Simplifying 8c2 + -13c = -3 Reorder the terms: -13c + 8c2 = -3 Solving -13c + 8c2 = -3 Solving for variable 'c'. Reorder the terms: 3 + -13c + 8c2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + -13c + 8c2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + -1.625c + c2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + -1.625c + -0.375 + c2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + -1.625c + c2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + -1.625c + c2 = 0 + -0.375 -1.625c + c2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 -1.625c + c2 = -0.375 The c term is -1.625c. Take half its coefficient (-0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. -1.625c + 0.66015625 + c2 = -0.375 + 0.66015625 Reorder the terms: 0.66015625 + -1.625c + c2 = -0.375 + 0.66015625 Combine like terms: -0.375 + 0.66015625 = 0.28515625 0.66015625 + -1.625c + c2 = 0.28515625 Factor a perfect square on the left side: (c + -0.8125)(c + -0.8125) = 0.28515625 Calculate the square root of the right side: 0.534000234 Break this problem into two subproblems by setting (c + -0.8125) equal to 0.534000234 and -0.534000234.Subproblem 1
c + -0.8125 = 0.534000234 Simplifying c + -0.8125 = 0.534000234 Reorder the terms: -0.8125 + c = 0.534000234 Solving -0.8125 + c = 0.534000234 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + c = 0.534000234 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + c = 0.534000234 + 0.8125 c = 0.534000234 + 0.8125 Combine like terms: 0.534000234 + 0.8125 = 1.346500234 c = 1.346500234 Simplifying c = 1.346500234Subproblem 2
c + -0.8125 = -0.534000234 Simplifying c + -0.8125 = -0.534000234 Reorder the terms: -0.8125 + c = -0.534000234 Solving -0.8125 + c = -0.534000234 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + c = -0.534000234 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + c = -0.534000234 + 0.8125 c = -0.534000234 + 0.8125 Combine like terms: -0.534000234 + 0.8125 = 0.278499766 c = 0.278499766 Simplifying c = 0.278499766Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.346500234, 0.278499766}
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