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Simplifying 18x2 + -59x + 33 = 0 Reorder the terms: 33 + -59x + 18x2 = 0 Solving 33 + -59x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 1.833333333 + -3.277777778x + x2 = 0 Move the constant term to the right: Add '-1.833333333' to each side of the equation. 1.833333333 + -3.277777778x + -1.833333333 + x2 = 0 + -1.833333333 Reorder the terms: 1.833333333 + -1.833333333 + -3.277777778x + x2 = 0 + -1.833333333 Combine like terms: 1.833333333 + -1.833333333 = 0.000000000 0.000000000 + -3.277777778x + x2 = 0 + -1.833333333 -3.277777778x + x2 = 0 + -1.833333333 Combine like terms: 0 + -1.833333333 = -1.833333333 -3.277777778x + x2 = -1.833333333 The x term is -3.277777778x. Take half its coefficient (-1.638888889). Square it (2.685956790) and add it to both sides. Add '2.685956790' to each side of the equation. -3.277777778x + 2.685956790 + x2 = -1.833333333 + 2.685956790 Reorder the terms: 2.685956790 + -3.277777778x + x2 = -1.833333333 + 2.685956790 Combine like terms: -1.833333333 + 2.685956790 = 0.852623457 2.685956790 + -3.277777778x + x2 = 0.852623457 Factor a perfect square on the left side: (x + -1.638888889)(x + -1.638888889) = 0.852623457 Calculate the square root of the right side: 0.923376119 Break this problem into two subproblems by setting (x + -1.638888889) equal to 0.923376119 and -0.923376119.Subproblem 1
x + -1.638888889 = 0.923376119 Simplifying x + -1.638888889 = 0.923376119 Reorder the terms: -1.638888889 + x = 0.923376119 Solving -1.638888889 + x = 0.923376119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.638888889' to each side of the equation. -1.638888889 + 1.638888889 + x = 0.923376119 + 1.638888889 Combine like terms: -1.638888889 + 1.638888889 = 0.000000000 0.000000000 + x = 0.923376119 + 1.638888889 x = 0.923376119 + 1.638888889 Combine like terms: 0.923376119 + 1.638888889 = 2.562265008 x = 2.562265008 Simplifying x = 2.562265008Subproblem 2
x + -1.638888889 = -0.923376119 Simplifying x + -1.638888889 = -0.923376119 Reorder the terms: -1.638888889 + x = -0.923376119 Solving -1.638888889 + x = -0.923376119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.638888889' to each side of the equation. -1.638888889 + 1.638888889 + x = -0.923376119 + 1.638888889 Combine like terms: -1.638888889 + 1.638888889 = 0.000000000 0.000000000 + x = -0.923376119 + 1.638888889 x = -0.923376119 + 1.638888889 Combine like terms: -0.923376119 + 1.638888889 = 0.71551277 x = 0.71551277 Simplifying x = 0.71551277Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.562265008, 0.71551277}
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