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Simplifying 36x2 = x + 8 Reorder the terms: 36x2 = 8 + x Solving 36x2 = 8 + x Solving for variable 'x'. Reorder the terms: -8 + -1x + 36x2 = 8 + x + -8 + -1x Reorder the terms: -8 + -1x + 36x2 = 8 + -8 + x + -1x Combine like terms: 8 + -8 = 0 -8 + -1x + 36x2 = 0 + x + -1x -8 + -1x + 36x2 = x + -1x Combine like terms: x + -1x = 0 -8 + -1x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.2222222222 + -0.02777777778x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -0.02777777778x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -0.02777777778x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -0.02777777778x + x2 = 0 + 0.2222222222 -0.02777777778x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -0.02777777778x + x2 = 0.2222222222 The x term is -0.02777777778x. Take half its coefficient (-0.01388888889). Square it (0.0001929012346) and add it to both sides. Add '0.0001929012346' to each side of the equation. -0.02777777778x + 0.0001929012346 + x2 = 0.2222222222 + 0.0001929012346 Reorder the terms: 0.0001929012346 + -0.02777777778x + x2 = 0.2222222222 + 0.0001929012346 Combine like terms: 0.2222222222 + 0.0001929012346 = 0.2224151234346 0.0001929012346 + -0.02777777778x + x2 = 0.2224151234346 Factor a perfect square on the left side: (x + -0.01388888889)(x + -0.01388888889) = 0.2224151234346 Calculate the square root of the right side: 0.471609079 Break this problem into two subproblems by setting (x + -0.01388888889) equal to 0.471609079 and -0.471609079.Subproblem 1
x + -0.01388888889 = 0.471609079 Simplifying x + -0.01388888889 = 0.471609079 Reorder the terms: -0.01388888889 + x = 0.471609079 Solving -0.01388888889 + x = 0.471609079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01388888889' to each side of the equation. -0.01388888889 + 0.01388888889 + x = 0.471609079 + 0.01388888889 Combine like terms: -0.01388888889 + 0.01388888889 = 0.00000000000 0.00000000000 + x = 0.471609079 + 0.01388888889 x = 0.471609079 + 0.01388888889 Combine like terms: 0.471609079 + 0.01388888889 = 0.48549796789 x = 0.48549796789 Simplifying x = 0.48549796789Subproblem 2
x + -0.01388888889 = -0.471609079 Simplifying x + -0.01388888889 = -0.471609079 Reorder the terms: -0.01388888889 + x = -0.471609079 Solving -0.01388888889 + x = -0.471609079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01388888889' to each side of the equation. -0.01388888889 + 0.01388888889 + x = -0.471609079 + 0.01388888889 Combine like terms: -0.01388888889 + 0.01388888889 = 0.00000000000 0.00000000000 + x = -0.471609079 + 0.01388888889 x = -0.471609079 + 0.01388888889 Combine like terms: -0.471609079 + 0.01388888889 = -0.45772019011 x = -0.45772019011 Simplifying x = -0.45772019011Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.48549796789, -0.45772019011}
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