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Simplifying 0.16c2 + 0.40c + 0.25 = 0 Reorder the terms: 0.25 + 0.40c + 0.16c2 = 0 Solving 0.25 + 0.40c + 0.16c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 0.16 the coefficient of the squared term: Divide each side by '0.16'. 1.5625 + 2.5c + c2 = 0 Move the constant term to the right: Add '-1.5625' to each side of the equation. 1.5625 + 2.5c + -1.5625 + c2 = 0 + -1.5625 Reorder the terms: 1.5625 + -1.5625 + 2.5c + c2 = 0 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + 2.5c + c2 = 0 + -1.5625 2.5c + c2 = 0 + -1.5625 Combine like terms: 0 + -1.5625 = -1.5625 2.5c + c2 = -1.5625 The c term is 2.5c. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5c + 1.5625 + c2 = -1.5625 + 1.5625 Reorder the terms: 1.5625 + 2.5c + c2 = -1.5625 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 1.5625 + 2.5c + c2 = 0.0000 Factor a perfect square on the left side: (c + 1.25)(c + 1.25) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (c + 1.25) equal to 0.0000 and 0.0000.Subproblem 1
c + 1.25 = 0.0000 Simplifying c + 1.25 = 0.0000 Reorder the terms: 1.25 + c = 0.0000 Solving 1.25 + c = 0.0000 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + c = 0.0000 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + c = 0.0000 + -1.25 c = 0.0000 + -1.25 Combine like terms: 0.0000 + -1.25 = -1.25 c = -1.25 Simplifying c = -1.25Subproblem 2
c + 1.25 = 0.0000 Simplifying c + 1.25 = 0.0000 Reorder the terms: 1.25 + c = 0.0000 Solving 1.25 + c = 0.0000 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + c = 0.0000 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + c = 0.0000 + -1.25 c = 0.0000 + -1.25 Combine like terms: 0.0000 + -1.25 = -1.25 c = -1.25 Simplifying c = -1.25Solution
The solution to the problem is based on the solutions from the subproblems. c = {-1.25, -1.25}
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