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Simplifying 9x2 + 46x + -5 = 0 Reorder the terms: -5 + 46x + 9x2 = 0 Solving -5 + 46x + 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'. -0.5555555556 + 5.111111111x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 5.111111111x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 5.111111111x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 5.111111111x + x2 = 0 + 0.5555555556 5.111111111x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 5.111111111x + x2 = 0.5555555556 The x term is 5.111111111x. Take half its coefficient (2.555555556). Square it (6.530864200) and add it to both sides. Add '6.530864200' to each side of the equation. 5.111111111x + 6.530864200 + x2 = 0.5555555556 + 6.530864200 Reorder the terms: 6.530864200 + 5.111111111x + x2 = 0.5555555556 + 6.530864200 Combine like terms: 0.5555555556 + 6.530864200 = 7.0864197556 6.530864200 + 5.111111111x + x2 = 7.0864197556 Factor a perfect square on the left side: (x + 2.555555556)(x + 2.555555556) = 7.0864197556 Calculate the square root of the right side: 2.662033012 Break this problem into two subproblems by setting (x + 2.555555556) equal to 2.662033012 and -2.662033012.Subproblem 1
x + 2.555555556 = 2.662033012 Simplifying x + 2.555555556 = 2.662033012 Reorder the terms: 2.555555556 + x = 2.662033012 Solving 2.555555556 + x = 2.662033012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.555555556' to each side of the equation. 2.555555556 + -2.555555556 + x = 2.662033012 + -2.555555556 Combine like terms: 2.555555556 + -2.555555556 = 0.000000000 0.000000000 + x = 2.662033012 + -2.555555556 x = 2.662033012 + -2.555555556 Combine like terms: 2.662033012 + -2.555555556 = 0.106477456 x = 0.106477456 Simplifying x = 0.106477456Subproblem 2
x + 2.555555556 = -2.662033012 Simplifying x + 2.555555556 = -2.662033012 Reorder the terms: 2.555555556 + x = -2.662033012 Solving 2.555555556 + x = -2.662033012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.555555556' to each side of the equation. 2.555555556 + -2.555555556 + x = -2.662033012 + -2.555555556 Combine like terms: 2.555555556 + -2.555555556 = 0.000000000 0.000000000 + x = -2.662033012 + -2.555555556 x = -2.662033012 + -2.555555556 Combine like terms: -2.662033012 + -2.555555556 = -5.217588568 x = -5.217588568 Simplifying x = -5.217588568Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.106477456, -5.217588568}
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