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Simplifying -0.5c2 + 1.50c + 250 = 0 Reorder the terms: 250 + 1.50c + -0.5c2 = 0 Solving 250 + 1.50c + -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'. -500 + -3c + c2 = 0 Move the constant term to the right: Add '500' to each side of the equation. -500 + -3c + 500 + c2 = 0 + 500 Reorder the terms: -500 + 500 + -3c + c2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + -3c + c2 = 0 + 500 -3c + c2 = 0 + 500 Combine like terms: 0 + 500 = 500 -3c + c2 = 500 The c term is -3c. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3c + 2.25 + c2 = 500 + 2.25 Reorder the terms: 2.25 + -3c + c2 = 500 + 2.25 Combine like terms: 500 + 2.25 = 502.25 2.25 + -3c + c2 = 502.25 Factor a perfect square on the left side: (c + -1.5)(c + -1.5) = 502.25 Calculate the square root of the right side: 22.410934831 Break this problem into two subproblems by setting (c + -1.5) equal to 22.410934831 and -22.410934831.Subproblem 1
c + -1.5 = 22.410934831 Simplifying c + -1.5 = 22.410934831 Reorder the terms: -1.5 + c = 22.410934831 Solving -1.5 + c = 22.410934831 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + c = 22.410934831 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + c = 22.410934831 + 1.5 c = 22.410934831 + 1.5 Combine like terms: 22.410934831 + 1.5 = 23.910934831 c = 23.910934831 Simplifying c = 23.910934831Subproblem 2
c + -1.5 = -22.410934831 Simplifying c + -1.5 = -22.410934831 Reorder the terms: -1.5 + c = -22.410934831 Solving -1.5 + c = -22.410934831 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + c = -22.410934831 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + c = -22.410934831 + 1.5 c = -22.410934831 + 1.5 Combine like terms: -22.410934831 + 1.5 = -20.910934831 c = -20.910934831 Simplifying c = -20.910934831Solution
The solution to the problem is based on the solutions from the subproblems. c = {23.910934831, -20.910934831}
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