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Simplifying 0.5c2 + 2c + 0.75 = 0 Reorder the terms: 0.75 + 2c + 0.5c2 = 0 Solving 0.75 + 2c + 0.5c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 1.5 + 4c + c2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 4c + -1.5 + c2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 4c + c2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 4c + c2 = 0 + -1.5 4c + c2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 4c + c2 = -1.5 The c term is 4c. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4c + 4 + c2 = -1.5 + 4 Reorder the terms: 4 + 4c + c2 = -1.5 + 4 Combine like terms: -1.5 + 4 = 2.5 4 + 4c + c2 = 2.5 Factor a perfect square on the left side: (c + 2)(c + 2) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (c + 2) equal to 1.58113883 and -1.58113883.Subproblem 1
c + 2 = 1.58113883 Simplifying c + 2 = 1.58113883 Reorder the terms: 2 + c = 1.58113883 Solving 2 + c = 1.58113883 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = 1.58113883 + -2 Combine like terms: 2 + -2 = 0 0 + c = 1.58113883 + -2 c = 1.58113883 + -2 Combine like terms: 1.58113883 + -2 = -0.41886117 c = -0.41886117 Simplifying c = -0.41886117Subproblem 2
c + 2 = -1.58113883 Simplifying c + 2 = -1.58113883 Reorder the terms: 2 + c = -1.58113883 Solving 2 + c = -1.58113883 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = -1.58113883 + -2 Combine like terms: 2 + -2 = 0 0 + c = -1.58113883 + -2 c = -1.58113883 + -2 Combine like terms: -1.58113883 + -2 = -3.58113883 c = -3.58113883 Simplifying c = -3.58113883Solution
The solution to the problem is based on the solutions from the subproblems. c = {-0.41886117, -3.58113883}
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