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Simplifying 9x2 + 31x + -46 = 0 Reorder the terms: -46 + 31x + 9x2 = 0 Solving -46 + 31x + 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'. -5.111111111 + 3.444444444x + x2 = 0 Move the constant term to the right: Add '5.111111111' to each side of the equation. -5.111111111 + 3.444444444x + 5.111111111 + x2 = 0 + 5.111111111 Reorder the terms: -5.111111111 + 5.111111111 + 3.444444444x + x2 = 0 + 5.111111111 Combine like terms: -5.111111111 + 5.111111111 = 0.000000000 0.000000000 + 3.444444444x + x2 = 0 + 5.111111111 3.444444444x + x2 = 0 + 5.111111111 Combine like terms: 0 + 5.111111111 = 5.111111111 3.444444444x + x2 = 5.111111111 The x term is 3.444444444x. Take half its coefficient (1.722222222). Square it (2.966049382) and add it to both sides. Add '2.966049382' to each side of the equation. 3.444444444x + 2.966049382 + x2 = 5.111111111 + 2.966049382 Reorder the terms: 2.966049382 + 3.444444444x + x2 = 5.111111111 + 2.966049382 Combine like terms: 5.111111111 + 2.966049382 = 8.077160493 2.966049382 + 3.444444444x + x2 = 8.077160493 Factor a perfect square on the left side: (x + 1.722222222)(x + 1.722222222) = 8.077160493 Calculate the square root of the right side: 2.842034569 Break this problem into two subproblems by setting (x + 1.722222222) equal to 2.842034569 and -2.842034569.Subproblem 1
x + 1.722222222 = 2.842034569 Simplifying x + 1.722222222 = 2.842034569 Reorder the terms: 1.722222222 + x = 2.842034569 Solving 1.722222222 + x = 2.842034569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.722222222' to each side of the equation. 1.722222222 + -1.722222222 + x = 2.842034569 + -1.722222222 Combine like terms: 1.722222222 + -1.722222222 = 0.000000000 0.000000000 + x = 2.842034569 + -1.722222222 x = 2.842034569 + -1.722222222 Combine like terms: 2.842034569 + -1.722222222 = 1.119812347 x = 1.119812347 Simplifying x = 1.119812347Subproblem 2
x + 1.722222222 = -2.842034569 Simplifying x + 1.722222222 = -2.842034569 Reorder the terms: 1.722222222 + x = -2.842034569 Solving 1.722222222 + x = -2.842034569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.722222222' to each side of the equation. 1.722222222 + -1.722222222 + x = -2.842034569 + -1.722222222 Combine like terms: 1.722222222 + -1.722222222 = 0.000000000 0.000000000 + x = -2.842034569 + -1.722222222 x = -2.842034569 + -1.722222222 Combine like terms: -2.842034569 + -1.722222222 = -4.564256791 x = -4.564256791 Simplifying x = -4.564256791Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.119812347, -4.564256791}
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