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Simplifying 24x2 + -44x + -74 = 0 Reorder the terms: -74 + -44x + 24x2 = 0 Solving -74 + -44x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-37 + -22x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-37 + -22x + 12x2)' equal to zero and attempt to solve: Simplifying -37 + -22x + 12x2 = 0 Solving -37 + -22x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -3.083333333 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '3.083333333' to each side of the equation. -3.083333333 + -1.833333333x + 3.083333333 + x2 = 0 + 3.083333333 Reorder the terms: -3.083333333 + 3.083333333 + -1.833333333x + x2 = 0 + 3.083333333 Combine like terms: -3.083333333 + 3.083333333 = 0.000000000 0.000000000 + -1.833333333x + x2 = 0 + 3.083333333 -1.833333333x + x2 = 0 + 3.083333333 Combine like terms: 0 + 3.083333333 = 3.083333333 -1.833333333x + x2 = 3.083333333 The x term is -1.833333333x. Take half its coefficient (-0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. -1.833333333x + 0.8402777775 + x2 = 3.083333333 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = 3.083333333 + 0.8402777775 Combine like terms: 3.083333333 + 0.8402777775 = 3.9236111105 0.8402777775 + -1.833333333x + x2 = 3.9236111105 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 3.9236111105 Calculate the square root of the right side: 1.980810721 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 1.980810721 and -1.980810721.Subproblem 1
x + -0.9166666665 = 1.980810721 Simplifying x + -0.9166666665 = 1.980810721 Reorder the terms: -0.9166666665 + x = 1.980810721 Solving -0.9166666665 + x = 1.980810721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = 1.980810721 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 1.980810721 + 0.9166666665 x = 1.980810721 + 0.9166666665 Combine like terms: 1.980810721 + 0.9166666665 = 2.8974773875 x = 2.8974773875 Simplifying x = 2.8974773875Subproblem 2
x + -0.9166666665 = -1.980810721 Simplifying x + -0.9166666665 = -1.980810721 Reorder the terms: -0.9166666665 + x = -1.980810721 Solving -0.9166666665 + x = -1.980810721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = -1.980810721 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -1.980810721 + 0.9166666665 x = -1.980810721 + 0.9166666665 Combine like terms: -1.980810721 + 0.9166666665 = -1.0641440545 x = -1.0641440545 Simplifying x = -1.0641440545Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.8974773875, -1.0641440545}Solution
x = {2.8974773875, -1.0641440545}
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