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Simplifying (2c2 + 7c + -1) + -1(c2 + -10c + 4) = 0 Reorder the terms: (-1 + 7c + 2c2) + -1(c2 + -10c + 4) = 0 Remove parenthesis around (-1 + 7c + 2c2) -1 + 7c + 2c2 + -1(c2 + -10c + 4) = 0 Reorder the terms: -1 + 7c + 2c2 + -1(4 + -10c + c2) = 0 -1 + 7c + 2c2 + (4 * -1 + -10c * -1 + c2 * -1) = 0 -1 + 7c + 2c2 + (-4 + 10c + -1c2) = 0 Reorder the terms: -1 + -4 + 7c + 10c + 2c2 + -1c2 = 0 Combine like terms: -1 + -4 = -5 -5 + 7c + 10c + 2c2 + -1c2 = 0 Combine like terms: 7c + 10c = 17c -5 + 17c + 2c2 + -1c2 = 0 Combine like terms: 2c2 + -1c2 = 1c2 -5 + 17c + 1c2 = 0 Solving -5 + 17c + 1c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 17c + 5 + c2 = 0 + 5 Reorder the terms: -5 + 5 + 17c + c2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 17c + c2 = 0 + 5 17c + c2 = 0 + 5 Combine like terms: 0 + 5 = 5 17c + c2 = 5 The c term is 17c. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17c + 72.25 + c2 = 5 + 72.25 Reorder the terms: 72.25 + 17c + c2 = 5 + 72.25 Combine like terms: 5 + 72.25 = 77.25 72.25 + 17c + c2 = 77.25 Factor a perfect square on the left side: (c + 8.5)(c + 8.5) = 77.25 Calculate the square root of the right side: 8.789197916 Break this problem into two subproblems by setting (c + 8.5) equal to 8.789197916 and -8.789197916.Subproblem 1
c + 8.5 = 8.789197916 Simplifying c + 8.5 = 8.789197916 Reorder the terms: 8.5 + c = 8.789197916 Solving 8.5 + c = 8.789197916 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + c = 8.789197916 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + c = 8.789197916 + -8.5 c = 8.789197916 + -8.5 Combine like terms: 8.789197916 + -8.5 = 0.289197916 c = 0.289197916 Simplifying c = 0.289197916Subproblem 2
c + 8.5 = -8.789197916 Simplifying c + 8.5 = -8.789197916 Reorder the terms: 8.5 + c = -8.789197916 Solving 8.5 + c = -8.789197916 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + c = -8.789197916 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + c = -8.789197916 + -8.5 c = -8.789197916 + -8.5 Combine like terms: -8.789197916 + -8.5 = -17.289197916 c = -17.289197916 Simplifying c = -17.289197916Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.289197916, -17.289197916}
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