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Simplifying 25c2 + -10c + -1 = 0 Reorder the terms: -1 + -10c + 25c2 = 0 Solving -1 + -10c + 25c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.04 + -0.4c + c2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + -0.4c + 0.04 + c2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + -0.4c + c2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + -0.4c + c2 = 0 + 0.04 -0.4c + c2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 -0.4c + c2 = 0.04 The c term is -0.4c. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4c + 0.04 + c2 = 0.04 + 0.04 Reorder the terms: 0.04 + -0.4c + c2 = 0.04 + 0.04 Combine like terms: 0.04 + 0.04 = 0.08 0.04 + -0.4c + c2 = 0.08 Factor a perfect square on the left side: (c + -0.2)(c + -0.2) = 0.08 Calculate the square root of the right side: 0.282842712 Break this problem into two subproblems by setting (c + -0.2) equal to 0.282842712 and -0.282842712.Subproblem 1
c + -0.2 = 0.282842712 Simplifying c + -0.2 = 0.282842712 Reorder the terms: -0.2 + c = 0.282842712 Solving -0.2 + c = 0.282842712 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + c = 0.282842712 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + c = 0.282842712 + 0.2 c = 0.282842712 + 0.2 Combine like terms: 0.282842712 + 0.2 = 0.482842712 c = 0.482842712 Simplifying c = 0.482842712Subproblem 2
c + -0.2 = -0.282842712 Simplifying c + -0.2 = -0.282842712 Reorder the terms: -0.2 + c = -0.282842712 Solving -0.2 + c = -0.282842712 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + c = -0.282842712 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + c = -0.282842712 + 0.2 c = -0.282842712 + 0.2 Combine like terms: -0.282842712 + 0.2 = -0.082842712 c = -0.082842712 Simplifying c = -0.082842712Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.482842712, -0.082842712}
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