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Simplifying 2c2 + -7c + -200 = 0 Reorder the terms: -200 + -7c + 2c2 = 0 Solving -200 + -7c + 2c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -100 + -3.5c + c2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -3.5c + 100 + c2 = 0 + 100 Reorder the terms: -100 + 100 + -3.5c + c2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -3.5c + c2 = 0 + 100 -3.5c + c2 = 0 + 100 Combine like terms: 0 + 100 = 100 -3.5c + c2 = 100 The c term is -3.5c. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5c + 3.0625 + c2 = 100 + 3.0625 Reorder the terms: 3.0625 + -3.5c + c2 = 100 + 3.0625 Combine like terms: 100 + 3.0625 = 103.0625 3.0625 + -3.5c + c2 = 103.0625 Factor a perfect square on the left side: (c + -1.75)(c + -1.75) = 103.0625 Calculate the square root of the right side: 10.151970252 Break this problem into two subproblems by setting (c + -1.75) equal to 10.151970252 and -10.151970252.Subproblem 1
c + -1.75 = 10.151970252 Simplifying c + -1.75 = 10.151970252 Reorder the terms: -1.75 + c = 10.151970252 Solving -1.75 + c = 10.151970252 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + c = 10.151970252 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + c = 10.151970252 + 1.75 c = 10.151970252 + 1.75 Combine like terms: 10.151970252 + 1.75 = 11.901970252 c = 11.901970252 Simplifying c = 11.901970252Subproblem 2
c + -1.75 = -10.151970252 Simplifying c + -1.75 = -10.151970252 Reorder the terms: -1.75 + c = -10.151970252 Solving -1.75 + c = -10.151970252 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + c = -10.151970252 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + c = -10.151970252 + 1.75 c = -10.151970252 + 1.75 Combine like terms: -10.151970252 + 1.75 = -8.401970252 c = -8.401970252 Simplifying c = -8.401970252Solution
The solution to the problem is based on the solutions from the subproblems. c = {11.901970252, -8.401970252}
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