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Simplifying 0.4c2 + -7c + -25 = 0 Reorder the terms: -25 + -7c + 0.4c2 = 0 Solving -25 + -7c + 0.4c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. -62.5 + -17.5c + c2 = 0 Move the constant term to the right: Add '62.5' to each side of the equation. -62.5 + -17.5c + 62.5 + c2 = 0 + 62.5 Reorder the terms: -62.5 + 62.5 + -17.5c + c2 = 0 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + -17.5c + c2 = 0 + 62.5 -17.5c + c2 = 0 + 62.5 Combine like terms: 0 + 62.5 = 62.5 -17.5c + c2 = 62.5 The c term is -17.5c. Take half its coefficient (-8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. -17.5c + 76.5625 + c2 = 62.5 + 76.5625 Reorder the terms: 76.5625 + -17.5c + c2 = 62.5 + 76.5625 Combine like terms: 62.5 + 76.5625 = 139.0625 76.5625 + -17.5c + c2 = 139.0625 Factor a perfect square on the left side: (c + -8.75)(c + -8.75) = 139.0625 Calculate the square root of the right side: 11.792476415 Break this problem into two subproblems by setting (c + -8.75) equal to 11.792476415 and -11.792476415.Subproblem 1
c + -8.75 = 11.792476415 Simplifying c + -8.75 = 11.792476415 Reorder the terms: -8.75 + c = 11.792476415 Solving -8.75 + c = 11.792476415 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + c = 11.792476415 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + c = 11.792476415 + 8.75 c = 11.792476415 + 8.75 Combine like terms: 11.792476415 + 8.75 = 20.542476415 c = 20.542476415 Simplifying c = 20.542476415Subproblem 2
c + -8.75 = -11.792476415 Simplifying c + -8.75 = -11.792476415 Reorder the terms: -8.75 + c = -11.792476415 Solving -8.75 + c = -11.792476415 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + c = -11.792476415 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + c = -11.792476415 + 8.75 c = -11.792476415 + 8.75 Combine like terms: -11.792476415 + 8.75 = -3.042476415 c = -3.042476415 Simplifying c = -3.042476415Solution
The solution to the problem is based on the solutions from the subproblems. c = {20.542476415, -3.042476415}
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