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Simplifying 2c2 = 3 + 4c Solving 2c2 = 3 + 4c Solving for variable 'c'. Reorder the terms: -3 + -4c + 2c2 = 3 + 4c + -3 + -4c Reorder the terms: -3 + -4c + 2c2 = 3 + -3 + 4c + -4c Combine like terms: 3 + -3 = 0 -3 + -4c + 2c2 = 0 + 4c + -4c -3 + -4c + 2c2 = 4c + -4c Combine like terms: 4c + -4c = 0 -3 + -4c + 2c2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -2c + c2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2c + 1.5 + c2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2c + c2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2c + c2 = 0 + 1.5 -2c + c2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2c + c2 = 1.5 The c term is -2c. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2c + 1 + c2 = 1.5 + 1 Reorder the terms: 1 + -2c + c2 = 1.5 + 1 Combine like terms: 1.5 + 1 = 2.5 1 + -2c + c2 = 2.5 Factor a perfect square on the left side: (c + -1)(c + -1) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (c + -1) equal to 1.58113883 and -1.58113883.Subproblem 1
c + -1 = 1.58113883 Simplifying c + -1 = 1.58113883 Reorder the terms: -1 + c = 1.58113883 Solving -1 + c = 1.58113883 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + c = 1.58113883 + 1 Combine like terms: -1 + 1 = 0 0 + c = 1.58113883 + 1 c = 1.58113883 + 1 Combine like terms: 1.58113883 + 1 = 2.58113883 c = 2.58113883 Simplifying c = 2.58113883Subproblem 2
c + -1 = -1.58113883 Simplifying c + -1 = -1.58113883 Reorder the terms: -1 + c = -1.58113883 Solving -1 + c = -1.58113883 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + c = -1.58113883 + 1 Combine like terms: -1 + 1 = 0 0 + c = -1.58113883 + 1 c = -1.58113883 + 1 Combine like terms: -1.58113883 + 1 = -0.58113883 c = -0.58113883 Simplifying c = -0.58113883Solution
The solution to the problem is based on the solutions from the subproblems. c = {2.58113883, -0.58113883}
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