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Simplifying 9x2 + -25x + 17 = 0 Reorder the terms: 17 + -25x + 9x2 = 0 Solving 17 + -25x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.888888889 + -2.777777778x + x2 = 0 Move the constant term to the right: Add '-1.888888889' to each side of the equation. 1.888888889 + -2.777777778x + -1.888888889 + x2 = 0 + -1.888888889 Reorder the terms: 1.888888889 + -1.888888889 + -2.777777778x + x2 = 0 + -1.888888889 Combine like terms: 1.888888889 + -1.888888889 = 0.000000000 0.000000000 + -2.777777778x + x2 = 0 + -1.888888889 -2.777777778x + x2 = 0 + -1.888888889 Combine like terms: 0 + -1.888888889 = -1.888888889 -2.777777778x + x2 = -1.888888889 The x term is -2.777777778x. Take half its coefficient (-1.388888889). Square it (1.929012346) and add it to both sides. Add '1.929012346' to each side of the equation. -2.777777778x + 1.929012346 + x2 = -1.888888889 + 1.929012346 Reorder the terms: 1.929012346 + -2.777777778x + x2 = -1.888888889 + 1.929012346 Combine like terms: -1.888888889 + 1.929012346 = 0.040123457 1.929012346 + -2.777777778x + x2 = 0.040123457 Factor a perfect square on the left side: (x + -1.388888889)(x + -1.388888889) = 0.040123457 Calculate the square root of the right side: 0.200308405 Break this problem into two subproblems by setting (x + -1.388888889) equal to 0.200308405 and -0.200308405.Subproblem 1
x + -1.388888889 = 0.200308405 Simplifying x + -1.388888889 = 0.200308405 Reorder the terms: -1.388888889 + x = 0.200308405 Solving -1.388888889 + x = 0.200308405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + x = 0.200308405 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = 0.200308405 + 1.388888889 x = 0.200308405 + 1.388888889 Combine like terms: 0.200308405 + 1.388888889 = 1.589197294 x = 1.589197294 Simplifying x = 1.589197294Subproblem 2
x + -1.388888889 = -0.200308405 Simplifying x + -1.388888889 = -0.200308405 Reorder the terms: -1.388888889 + x = -0.200308405 Solving -1.388888889 + x = -0.200308405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + x = -0.200308405 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = -0.200308405 + 1.388888889 x = -0.200308405 + 1.388888889 Combine like terms: -0.200308405 + 1.388888889 = 1.188580484 x = 1.188580484 Simplifying x = 1.188580484Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.589197294, 1.188580484}
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