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Simplifying 18x2 + -32 = 1x + -18x2 Reorder the terms: -32 + 18x2 = 1x + -18x2 Solving -32 + 18x2 = 1x + -18x2 Solving for variable 'x'. Reorder the terms: -32 + -1x + 18x2 + 18x2 = 1x + -18x2 + -1x + 18x2 Combine like terms: 18x2 + 18x2 = 36x2 -32 + -1x + 36x2 = 1x + -18x2 + -1x + 18x2 Reorder the terms: -32 + -1x + 36x2 = 1x + -1x + -18x2 + 18x2 Combine like terms: 1x + -1x = 0 -32 + -1x + 36x2 = 0 + -18x2 + 18x2 -32 + -1x + 36x2 = -18x2 + 18x2 Combine like terms: -18x2 + 18x2 = 0 -32 + -1x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.8888888889 + -0.02777777778x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -0.02777777778x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -0.02777777778x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -0.02777777778x + x2 = 0 + 0.8888888889 -0.02777777778x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -0.02777777778x + x2 = 0.8888888889 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 = 0.8888888889 + 0.0001929012346 Reorder the terms: 0.0001929012346 + -0.02777777778x + x2 = 0.8888888889 + 0.0001929012346 Combine like terms: 0.8888888889 + 0.0001929012346 = 0.8890817901346 0.0001929012346 + -0.02777777778x + x2 = 0.8890817901346 Factor a perfect square on the left side: (x + -0.01388888889)(x + -0.01388888889) = 0.8890817901346 Calculate the square root of the right side: 0.942911337 Break this problem into two subproblems by setting (x + -0.01388888889) equal to 0.942911337 and -0.942911337.Subproblem 1
x + -0.01388888889 = 0.942911337 Simplifying x + -0.01388888889 = 0.942911337 Reorder the terms: -0.01388888889 + x = 0.942911337 Solving -0.01388888889 + x = 0.942911337 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 = 0.942911337 + 0.01388888889 Combine like terms: -0.01388888889 + 0.01388888889 = 0.00000000000 0.00000000000 + x = 0.942911337 + 0.01388888889 x = 0.942911337 + 0.01388888889 Combine like terms: 0.942911337 + 0.01388888889 = 0.95680022589 x = 0.95680022589 Simplifying x = 0.95680022589Subproblem 2
x + -0.01388888889 = -0.942911337 Simplifying x + -0.01388888889 = -0.942911337 Reorder the terms: -0.01388888889 + x = -0.942911337 Solving -0.01388888889 + x = -0.942911337 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 = -0.942911337 + 0.01388888889 Combine like terms: -0.01388888889 + 0.01388888889 = 0.00000000000 0.00000000000 + x = -0.942911337 + 0.01388888889 x = -0.942911337 + 0.01388888889 Combine like terms: -0.942911337 + 0.01388888889 = -0.92902244811 x = -0.92902244811 Simplifying x = -0.92902244811Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.95680022589, -0.92902244811}
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