Identify the conic section $$$\frac{617}{1000000000000} = \frac{500 x^{2}}{673} - x$$$

Identify and find the properties of the conic section $$$\frac{617}{1000000000000} = \frac{500 x^{2}}{673} - x$$$.

The general equation of a conic section is $$$A x^{2} + B x y + C y^{2} + D x + E y + F = 0$$$.

In our case, $$$A = \frac{500}{673}$$$, $$$B = 0$$$, $$$C = 0$$$, $$$D = -1$$$, $$$E = 0$$$, $$$F = - \frac{617}{1000000000000}$$$.

The discriminant of the conic section is $$$\Delta = 4 A C F - A E^{2} - B^{2} F + B D E - C D^{2} = 0$$$.

Next, $$$B^{2} - 4 A C = 0$$$.

Since $$$\Delta = 0$$$, this is the degenerated conic section.

Since $$$B^{2} - 4 A C = 0$$$, the equation represents two parallel lines.

$$$\frac{617}{1000000000000} = \frac{500 x^{2}}{673} - x$$$A represents a pair of the lines $$$x = - \frac{-33650000 + \sqrt{1132322502076205}}{50000000}$$$, $$$x = \frac{33650000 + \sqrt{1132322502076205}}{50000000}$$$A.

General form: $$$\frac{500 x^{2}}{673} - x - \frac{617}{1000000000000} = 0$$$A.

Factored form: $$$\left(50000000 x - 33650000 + \sqrt{1132322502076205}\right) \left(50000000 x - \sqrt{1132322502076205} - 33650000\right) = 0.$$$A

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