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Simplifying (-8c2 + 4c + 6) + -1(6c2 + 7c + -3) = 0 Reorder the terms: (6 + 4c + -8c2) + -1(6c2 + 7c + -3) = 0 Remove parenthesis around (6 + 4c + -8c2) 6 + 4c + -8c2 + -1(6c2 + 7c + -3) = 0 Reorder the terms: 6 + 4c + -8c2 + -1(-3 + 7c + 6c2) = 0 6 + 4c + -8c2 + (-3 * -1 + 7c * -1 + 6c2 * -1) = 0 6 + 4c + -8c2 + (3 + -7c + -6c2) = 0 Reorder the terms: 6 + 3 + 4c + -7c + -8c2 + -6c2 = 0 Combine like terms: 6 + 3 = 9 9 + 4c + -7c + -8c2 + -6c2 = 0 Combine like terms: 4c + -7c = -3c 9 + -3c + -8c2 + -6c2 = 0 Combine like terms: -8c2 + -6c2 = -14c2 9 + -3c + -14c2 = 0 Solving 9 + -3c + -14c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -0.6428571429 + 0.2142857143c + c2 = 0 Move the constant term to the right: Add '0.6428571429' to each side of the equation. -0.6428571429 + 0.2142857143c + 0.6428571429 + c2 = 0 + 0.6428571429 Reorder the terms: -0.6428571429 + 0.6428571429 + 0.2142857143c + c2 = 0 + 0.6428571429 Combine like terms: -0.6428571429 + 0.6428571429 = 0.0000000000 0.0000000000 + 0.2142857143c + c2 = 0 + 0.6428571429 0.2142857143c + c2 = 0 + 0.6428571429 Combine like terms: 0 + 0.6428571429 = 0.6428571429 0.2142857143c + c2 = 0.6428571429 The c term is 0.2142857143c. Take half its coefficient (0.1071428572). Square it (0.01147959185) and add it to both sides. Add '0.01147959185' to each side of the equation. 0.2142857143c + 0.01147959185 + c2 = 0.6428571429 + 0.01147959185 Reorder the terms: 0.01147959185 + 0.2142857143c + c2 = 0.6428571429 + 0.01147959185 Combine like terms: 0.6428571429 + 0.01147959185 = 0.65433673475 0.01147959185 + 0.2142857143c + c2 = 0.65433673475 Factor a perfect square on the left side: (c + 0.1071428572)(c + 0.1071428572) = 0.65433673475 Calculate the square root of the right side: 0.808910832 Break this problem into two subproblems by setting (c + 0.1071428572) equal to 0.808910832 and -0.808910832.Subproblem 1
c + 0.1071428572 = 0.808910832 Simplifying c + 0.1071428572 = 0.808910832 Reorder the terms: 0.1071428572 + c = 0.808910832 Solving 0.1071428572 + c = 0.808910832 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.1071428572' to each side of the equation. 0.1071428572 + -0.1071428572 + c = 0.808910832 + -0.1071428572 Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000 0.0000000000 + c = 0.808910832 + -0.1071428572 c = 0.808910832 + -0.1071428572 Combine like terms: 0.808910832 + -0.1071428572 = 0.7017679748 c = 0.7017679748 Simplifying c = 0.7017679748Subproblem 2
c + 0.1071428572 = -0.808910832 Simplifying c + 0.1071428572 = -0.808910832 Reorder the terms: 0.1071428572 + c = -0.808910832 Solving 0.1071428572 + c = -0.808910832 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.1071428572' to each side of the equation. 0.1071428572 + -0.1071428572 + c = -0.808910832 + -0.1071428572 Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000 0.0000000000 + c = -0.808910832 + -0.1071428572 c = -0.808910832 + -0.1071428572 Combine like terms: -0.808910832 + -0.1071428572 = -0.9160536892 c = -0.9160536892 Simplifying c = -0.9160536892Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.7017679748, -0.9160536892}
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