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Simplifying 18x2 + -59x = -34 Reorder the terms: -59x + 18x2 = -34 Solving -59x + 18x2 = -34 Solving for variable 'x'. Reorder the terms: 34 + -59x + 18x2 = -34 + 34 Combine like terms: -34 + 34 = 0 34 + -59x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 1.888888889 + -3.277777778x + x2 = 0 Move the constant term to the right: Add '-1.888888889' to each side of the equation. 1.888888889 + -3.277777778x + -1.888888889 + x2 = 0 + -1.888888889 Reorder the terms: 1.888888889 + -1.888888889 + -3.277777778x + x2 = 0 + -1.888888889 Combine like terms: 1.888888889 + -1.888888889 = 0.000000000 0.000000000 + -3.277777778x + x2 = 0 + -1.888888889 -3.277777778x + x2 = 0 + -1.888888889 Combine like terms: 0 + -1.888888889 = -1.888888889 -3.277777778x + x2 = -1.888888889 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 = -1.888888889 + 2.685956790 Reorder the terms: 2.685956790 + -3.277777778x + x2 = -1.888888889 + 2.685956790 Combine like terms: -1.888888889 + 2.685956790 = 0.797067901 2.685956790 + -3.277777778x + x2 = 0.797067901 Factor a perfect square on the left side: (x + -1.638888889)(x + -1.638888889) = 0.797067901 Calculate the square root of the right side: 0.892786593 Break this problem into two subproblems by setting (x + -1.638888889) equal to 0.892786593 and -0.892786593.Subproblem 1
x + -1.638888889 = 0.892786593 Simplifying x + -1.638888889 = 0.892786593 Reorder the terms: -1.638888889 + x = 0.892786593 Solving -1.638888889 + x = 0.892786593 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 = 0.892786593 + 1.638888889 Combine like terms: -1.638888889 + 1.638888889 = 0.000000000 0.000000000 + x = 0.892786593 + 1.638888889 x = 0.892786593 + 1.638888889 Combine like terms: 0.892786593 + 1.638888889 = 2.531675482 x = 2.531675482 Simplifying x = 2.531675482Subproblem 2
x + -1.638888889 = -0.892786593 Simplifying x + -1.638888889 = -0.892786593 Reorder the terms: -1.638888889 + x = -0.892786593 Solving -1.638888889 + x = -0.892786593 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 = -0.892786593 + 1.638888889 Combine like terms: -1.638888889 + 1.638888889 = 0.000000000 0.000000000 + x = -0.892786593 + 1.638888889 x = -0.892786593 + 1.638888889 Combine like terms: -0.892786593 + 1.638888889 = 0.746102296 x = 0.746102296 Simplifying x = 0.746102296Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.531675482, 0.746102296}
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