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Simplifying 9x2 + -38x + 1 = 0 Reorder the terms: 1 + -38x + 9x2 = 0 Solving 1 + -38x + 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'. 0.1111111111 + -4.222222222x + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + -4.222222222x + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + -4.222222222x + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + -4.222222222x + x2 = 0 + -0.1111111111 -4.222222222x + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 -4.222222222x + x2 = -0.1111111111 The x term is -4.222222222x. Take half its coefficient (-2.111111111). Square it (4.456790123) and add it to both sides. Add '4.456790123' to each side of the equation. -4.222222222x + 4.456790123 + x2 = -0.1111111111 + 4.456790123 Reorder the terms: 4.456790123 + -4.222222222x + x2 = -0.1111111111 + 4.456790123 Combine like terms: -0.1111111111 + 4.456790123 = 4.3456790119 4.456790123 + -4.222222222x + x2 = 4.3456790119 Factor a perfect square on the left side: (x + -2.111111111)(x + -2.111111111) = 4.3456790119 Calculate the square root of the right side: 2.084629226 Break this problem into two subproblems by setting (x + -2.111111111) equal to 2.084629226 and -2.084629226.Subproblem 1
x + -2.111111111 = 2.084629226 Simplifying x + -2.111111111 = 2.084629226 Reorder the terms: -2.111111111 + x = 2.084629226 Solving -2.111111111 + x = 2.084629226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.111111111' to each side of the equation. -2.111111111 + 2.111111111 + x = 2.084629226 + 2.111111111 Combine like terms: -2.111111111 + 2.111111111 = 0.000000000 0.000000000 + x = 2.084629226 + 2.111111111 x = 2.084629226 + 2.111111111 Combine like terms: 2.084629226 + 2.111111111 = 4.195740337 x = 4.195740337 Simplifying x = 4.195740337Subproblem 2
x + -2.111111111 = -2.084629226 Simplifying x + -2.111111111 = -2.084629226 Reorder the terms: -2.111111111 + x = -2.084629226 Solving -2.111111111 + x = -2.084629226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.111111111' to each side of the equation. -2.111111111 + 2.111111111 + x = -2.084629226 + 2.111111111 Combine like terms: -2.111111111 + 2.111111111 = 0.000000000 0.000000000 + x = -2.084629226 + 2.111111111 x = -2.084629226 + 2.111111111 Combine like terms: -2.084629226 + 2.111111111 = 0.026481885 x = 0.026481885 Simplifying x = 0.026481885Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.195740337, 0.026481885}
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