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Simplifying 18x2 + -33x = 4 Reorder the terms: -33x + 18x2 = 4 Solving -33x + 18x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + -33x + 18x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -33x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.2222222222 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -1.833333333x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -1.833333333x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -1.833333333x + x2 = 0 + 0.2222222222 -1.833333333x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -1.833333333x + x2 = 0.2222222222 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 = 0.2222222222 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = 0.2222222222 + 0.8402777775 Combine like terms: 0.2222222222 + 0.8402777775 = 1.0624999997 0.8402777775 + -1.833333333x + x2 = 1.0624999997 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 1.0624999997 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 1.030776406 and -1.030776406.Subproblem 1
x + -0.9166666665 = 1.030776406 Simplifying x + -0.9166666665 = 1.030776406 Reorder the terms: -0.9166666665 + x = 1.030776406 Solving -0.9166666665 + x = 1.030776406 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 = 1.030776406 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 1.030776406 + 0.9166666665 x = 1.030776406 + 0.9166666665 Combine like terms: 1.030776406 + 0.9166666665 = 1.9474430725 x = 1.9474430725 Simplifying x = 1.9474430725Subproblem 2
x + -0.9166666665 = -1.030776406 Simplifying x + -0.9166666665 = -1.030776406 Reorder the terms: -0.9166666665 + x = -1.030776406 Solving -0.9166666665 + x = -1.030776406 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 = -1.030776406 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -1.030776406 + 0.9166666665 x = -1.030776406 + 0.9166666665 Combine like terms: -1.030776406 + 0.9166666665 = -0.1141097395 x = -0.1141097395 Simplifying x = -0.1141097395Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9474430725, -0.1141097395}
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