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Simplifying 0.27(c2) + -1c + 0.27 = 0 Reorder the terms: 0.27 + -1c + 0.27c2 = 0 Solving 0.27 + -1c + 0.27c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 0.27 the coefficient of the squared term: Divide each side by '0.27'. 1 + -3.703703704c + c2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -3.703703704c + -1 + c2 = 0 + -1 Reorder the terms: 1 + -1 + -3.703703704c + c2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3.703703704c + c2 = 0 + -1 -3.703703704c + c2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3.703703704c + c2 = -1 The c term is -3.703703704c. Take half its coefficient (-1.851851852). Square it (3.429355282) and add it to both sides. Add '3.429355282' to each side of the equation. -3.703703704c + 3.429355282 + c2 = -1 + 3.429355282 Reorder the terms: 3.429355282 + -3.703703704c + c2 = -1 + 3.429355282 Combine like terms: -1 + 3.429355282 = 2.429355282 3.429355282 + -3.703703704c + c2 = 2.429355282 Factor a perfect square on the left side: (c + -1.851851852)(c + -1.851851852) = 2.429355282 Calculate the square root of the right side: 1.55863892 Break this problem into two subproblems by setting (c + -1.851851852) equal to 1.55863892 and -1.55863892.Subproblem 1
c + -1.851851852 = 1.55863892 Simplifying c + -1.851851852 = 1.55863892 Reorder the terms: -1.851851852 + c = 1.55863892 Solving -1.851851852 + c = 1.55863892 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.851851852' to each side of the equation. -1.851851852 + 1.851851852 + c = 1.55863892 + 1.851851852 Combine like terms: -1.851851852 + 1.851851852 = 0.000000000 0.000000000 + c = 1.55863892 + 1.851851852 c = 1.55863892 + 1.851851852 Combine like terms: 1.55863892 + 1.851851852 = 3.410490772 c = 3.410490772 Simplifying c = 3.410490772Subproblem 2
c + -1.851851852 = -1.55863892 Simplifying c + -1.851851852 = -1.55863892 Reorder the terms: -1.851851852 + c = -1.55863892 Solving -1.851851852 + c = -1.55863892 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.851851852' to each side of the equation. -1.851851852 + 1.851851852 + c = -1.55863892 + 1.851851852 Combine like terms: -1.851851852 + 1.851851852 = 0.000000000 0.000000000 + c = -1.55863892 + 1.851851852 c = -1.55863892 + 1.851851852 Combine like terms: -1.55863892 + 1.851851852 = 0.293212932 c = 0.293212932 Simplifying c = 0.293212932Solution
The solution to the problem is based on the solutions from the subproblems. c = {3.410490772, 0.293212932}
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