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Simplifying 7c2 + -2c = 1 Reorder the terms: -2c + 7c2 = 1 Solving -2c + 7c2 = 1 Solving for variable 'c'. Reorder the terms: -1 + -2c + 7c2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -2c + 7c2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -0.2857142857c + c2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.2857142857c + 0.1428571429 + c2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.2857142857c + c2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.2857142857c + c2 = 0 + 0.1428571429 -0.2857142857c + c2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.2857142857c + c2 = 0.1428571429 The c term is -0.2857142857c. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857c + 0.02040816328 + c2 = 0.1428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857c + c2 = 0.1428571429 + 0.02040816328 Combine like terms: 0.1428571429 + 0.02040816328 = 0.16326530618 0.02040816328 + -0.2857142857c + c2 = 0.16326530618 Factor a perfect square on the left side: (c + -0.1428571429)(c + -0.1428571429) = 0.16326530618 Calculate the square root of the right side: 0.404061018 Break this problem into two subproblems by setting (c + -0.1428571429) equal to 0.404061018 and -0.404061018.Subproblem 1
c + -0.1428571429 = 0.404061018 Simplifying c + -0.1428571429 = 0.404061018 Reorder the terms: -0.1428571429 + c = 0.404061018 Solving -0.1428571429 + c = 0.404061018 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + c = 0.404061018 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + c = 0.404061018 + 0.1428571429 c = 0.404061018 + 0.1428571429 Combine like terms: 0.404061018 + 0.1428571429 = 0.5469181609 c = 0.5469181609 Simplifying c = 0.5469181609Subproblem 2
c + -0.1428571429 = -0.404061018 Simplifying c + -0.1428571429 = -0.404061018 Reorder the terms: -0.1428571429 + c = -0.404061018 Solving -0.1428571429 + c = -0.404061018 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + c = -0.404061018 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + c = -0.404061018 + 0.1428571429 c = -0.404061018 + 0.1428571429 Combine like terms: -0.404061018 + 0.1428571429 = -0.2612038751 c = -0.2612038751 Simplifying c = -0.2612038751Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.5469181609, -0.2612038751}
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