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Simplifying 4c2 + 4c + -1 = 0 Reorder the terms: -1 + 4c + 4c2 = 0 Solving -1 + 4c + 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'. -0.25 + c + c2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + c + 0.25 + c2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + c + c2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + c + c2 = 0 + 0.25 c + c2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 c + c2 = 0.25 The c term is c. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + c2 = 0.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + c2 = 0.25 + 0.25 Combine like terms: 0.25 + 0.25 = 0.5 1.25 + c2 = 0.5 Factor a perfect square on the left side: (c + 0.5)(c + 0.5) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (c + 0.5) equal to 0.707106781 and -0.707106781.Subproblem 1
c + 0.5 = 0.707106781 Simplifying c + 0.5 = 0.707106781 Reorder the terms: 0.5 + c = 0.707106781 Solving 0.5 + c = 0.707106781 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + c = 0.707106781 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = 0.707106781 + -0.5 c = 0.707106781 + -0.5 Combine like terms: 0.707106781 + -0.5 = 0.207106781 c = 0.207106781 Simplifying c = 0.207106781Subproblem 2
c + 0.5 = -0.707106781 Simplifying c + 0.5 = -0.707106781 Reorder the terms: 0.5 + c = -0.707106781 Solving 0.5 + c = -0.707106781 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + c = -0.707106781 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = -0.707106781 + -0.5 c = -0.707106781 + -0.5 Combine like terms: -0.707106781 + -0.5 = -1.207106781 c = -1.207106781 Simplifying c = -1.207106781Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.207106781, -1.207106781}
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