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Simplifying 4c2 + 8c + -23 = 0 Reorder the terms: -23 + 8c + 4c2 = 0 Solving -23 + 8c + 4c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.75 + 2c + c2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + 2c + 5.75 + c2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + 2c + c2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + 2c + c2 = 0 + 5.75 2c + c2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 2c + c2 = 5.75 The c term is 2c. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2c + 1 + c2 = 5.75 + 1 Reorder the terms: 1 + 2c + c2 = 5.75 + 1 Combine like terms: 5.75 + 1 = 6.75 1 + 2c + c2 = 6.75 Factor a perfect square on the left side: (c + 1)(c + 1) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (c + 1) equal to 2.598076211 and -2.598076211.Subproblem 1
c + 1 = 2.598076211 Simplifying c + 1 = 2.598076211 Reorder the terms: 1 + c = 2.598076211 Solving 1 + c = 2.598076211 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + c = 2.598076211 + -1 Combine like terms: 1 + -1 = 0 0 + c = 2.598076211 + -1 c = 2.598076211 + -1 Combine like terms: 2.598076211 + -1 = 1.598076211 c = 1.598076211 Simplifying c = 1.598076211Subproblem 2
c + 1 = -2.598076211 Simplifying c + 1 = -2.598076211 Reorder the terms: 1 + c = -2.598076211 Solving 1 + c = -2.598076211 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + c = -2.598076211 + -1 Combine like terms: 1 + -1 = 0 0 + c = -2.598076211 + -1 c = -2.598076211 + -1 Combine like terms: -2.598076211 + -1 = -3.598076211 c = -3.598076211 Simplifying c = -3.598076211Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.598076211, -3.598076211}
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