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Simplifying (3c2 + 4c + -5) + -1(2c2 + -8c + 11) = 0 Reorder the terms: (-5 + 4c + 3c2) + -1(2c2 + -8c + 11) = 0 Remove parenthesis around (-5 + 4c + 3c2) -5 + 4c + 3c2 + -1(2c2 + -8c + 11) = 0 Reorder the terms: -5 + 4c + 3c2 + -1(11 + -8c + 2c2) = 0 -5 + 4c + 3c2 + (11 * -1 + -8c * -1 + 2c2 * -1) = 0 -5 + 4c + 3c2 + (-11 + 8c + -2c2) = 0 Reorder the terms: -5 + -11 + 4c + 8c + 3c2 + -2c2 = 0 Combine like terms: -5 + -11 = -16 -16 + 4c + 8c + 3c2 + -2c2 = 0 Combine like terms: 4c + 8c = 12c -16 + 12c + 3c2 + -2c2 = 0 Combine like terms: 3c2 + -2c2 = 1c2 -16 + 12c + 1c2 = 0 Solving -16 + 12c + 1c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 12c + 16 + c2 = 0 + 16 Reorder the terms: -16 + 16 + 12c + c2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 12c + c2 = 0 + 16 12c + c2 = 0 + 16 Combine like terms: 0 + 16 = 16 12c + c2 = 16 The c term is 12c. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12c + 36 + c2 = 16 + 36 Reorder the terms: 36 + 12c + c2 = 16 + 36 Combine like terms: 16 + 36 = 52 36 + 12c + c2 = 52 Factor a perfect square on the left side: (c + 6)(c + 6) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (c + 6) equal to 7.211102551 and -7.211102551.Subproblem 1
c + 6 = 7.211102551 Simplifying c + 6 = 7.211102551 Reorder the terms: 6 + c = 7.211102551 Solving 6 + c = 7.211102551 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + c = 7.211102551 + -6 Combine like terms: 6 + -6 = 0 0 + c = 7.211102551 + -6 c = 7.211102551 + -6 Combine like terms: 7.211102551 + -6 = 1.211102551 c = 1.211102551 Simplifying c = 1.211102551Subproblem 2
c + 6 = -7.211102551 Simplifying c + 6 = -7.211102551 Reorder the terms: 6 + c = -7.211102551 Solving 6 + c = -7.211102551 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + c = -7.211102551 + -6 Combine like terms: 6 + -6 = 0 0 + c = -7.211102551 + -6 c = -7.211102551 + -6 Combine like terms: -7.211102551 + -6 = -13.211102551 c = -13.211102551 Simplifying c = -13.211102551Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.211102551, -13.211102551}
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