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Simplifying 2c2 + 3.5c + -1 = 0 Reorder the terms: -1 + 3.5c + 2c2 = 0 Solving -1 + 3.5c + 2c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 1.75c + c2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.75c + 0.5 + c2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.75c + c2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.75c + c2 = 0 + 0.5 1.75c + c2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.75c + c2 = 0.5 The c term is 1.75c. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75c + 0.765625 + c2 = 0.5 + 0.765625 Reorder the terms: 0.765625 + 1.75c + c2 = 0.5 + 0.765625 Combine like terms: 0.5 + 0.765625 = 1.265625 0.765625 + 1.75c + c2 = 1.265625 Factor a perfect square on the left side: (c + 0.875)(c + 0.875) = 1.265625 Calculate the square root of the right side: 1.125 Break this problem into two subproblems by setting (c + 0.875) equal to 1.125 and -1.125.Subproblem 1
c + 0.875 = 1.125 Simplifying c + 0.875 = 1.125 Reorder the terms: 0.875 + c = 1.125 Solving 0.875 + c = 1.125 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + c = 1.125 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + c = 1.125 + -0.875 c = 1.125 + -0.875 Combine like terms: 1.125 + -0.875 = 0.25 c = 0.25 Simplifying c = 0.25Subproblem 2
c + 0.875 = -1.125 Simplifying c + 0.875 = -1.125 Reorder the terms: 0.875 + c = -1.125 Solving 0.875 + c = -1.125 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + c = -1.125 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + c = -1.125 + -0.875 c = -1.125 + -0.875 Combine like terms: -1.125 + -0.875 = -2 c = -2 Simplifying c = -2Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.25, -2}
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