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Simplifying (9x + -1)(2x + 1) = 2x Reorder the terms: (-1 + 9x)(2x + 1) = 2x Reorder the terms: (-1 + 9x)(1 + 2x) = 2x Multiply (-1 + 9x) * (1 + 2x) (-1(1 + 2x) + 9x * (1 + 2x)) = 2x ((1 * -1 + 2x * -1) + 9x * (1 + 2x)) = 2x ((-1 + -2x) + 9x * (1 + 2x)) = 2x (-1 + -2x + (1 * 9x + 2x * 9x)) = 2x (-1 + -2x + (9x + 18x2)) = 2x Combine like terms: -2x + 9x = 7x (-1 + 7x + 18x2) = 2x Solving -1 + 7x + 18x2 = 2x Solving for variable 'x'. Reorder the terms: -1 + 7x + -2x + 18x2 = 2x + -2x Combine like terms: 7x + -2x = 5x -1 + 5x + 18x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -1 + 5x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.05555555556 + 0.2777777778x + x2 = 0 Move the constant term to the right: Add '0.05555555556' to each side of the equation. -0.05555555556 + 0.2777777778x + 0.05555555556 + x2 = 0 + 0.05555555556 Reorder the terms: -0.05555555556 + 0.05555555556 + 0.2777777778x + x2 = 0 + 0.05555555556 Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000 0.00000000000 + 0.2777777778x + x2 = 0 + 0.05555555556 0.2777777778x + x2 = 0 + 0.05555555556 Combine like terms: 0 + 0.05555555556 = 0.05555555556 0.2777777778x + x2 = 0.05555555556 The x term is 0.2777777778x. Take half its coefficient (0.1388888889). Square it (0.01929012346) and add it to both sides. Add '0.01929012346' to each side of the equation. 0.2777777778x + 0.01929012346 + x2 = 0.05555555556 + 0.01929012346 Reorder the terms: 0.01929012346 + 0.2777777778x + x2 = 0.05555555556 + 0.01929012346 Combine like terms: 0.05555555556 + 0.01929012346 = 0.07484567902 0.01929012346 + 0.2777777778x + x2 = 0.07484567902 Factor a perfect square on the left side: (x + 0.1388888889)(x + 0.1388888889) = 0.07484567902 Calculate the square root of the right side: 0.273579383 Break this problem into two subproblems by setting (x + 0.1388888889) equal to 0.273579383 and -0.273579383.Subproblem 1
x + 0.1388888889 = 0.273579383 Simplifying x + 0.1388888889 = 0.273579383 Reorder the terms: 0.1388888889 + x = 0.273579383 Solving 0.1388888889 + x = 0.273579383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1388888889' to each side of the equation. 0.1388888889 + -0.1388888889 + x = 0.273579383 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + x = 0.273579383 + -0.1388888889 x = 0.273579383 + -0.1388888889 Combine like terms: 0.273579383 + -0.1388888889 = 0.1346904941 x = 0.1346904941 Simplifying x = 0.1346904941Subproblem 2
x + 0.1388888889 = -0.273579383 Simplifying x + 0.1388888889 = -0.273579383 Reorder the terms: 0.1388888889 + x = -0.273579383 Solving 0.1388888889 + x = -0.273579383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1388888889' to each side of the equation. 0.1388888889 + -0.1388888889 + x = -0.273579383 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + x = -0.273579383 + -0.1388888889 x = -0.273579383 + -0.1388888889 Combine like terms: -0.273579383 + -0.1388888889 = -0.4124682719 x = -0.4124682719 Simplifying x = -0.4124682719Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1346904941, -0.4124682719}
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