/ / ____\\ / / ____\\
| y*\-1 + I*\/ 19 /| | y*\1 + I*\/ 19 /|
|x - -----------------|*|x + ----------------|
\ 10 / \ 10 /
$$\left(x - \frac{y \left(-1 + \sqrt{19} i\right)}{10}\right) \left(x + \frac{y \left(1 + \sqrt{19} i\right)}{10}\right)$$
(x - y*(-1 + i*sqrt(19))/10)*(x + y*(1 + i*sqrt(19))/10)
The perfect square
Let's highlight the perfect square of the square three-member
$$- 5 x^{2} + \left(- x y - y^{2}\right)$$
Let us write down the identical expression
$$- 5 x^{2} + \left(- x y - y^{2}\right) = - \frac{19 y^{2}}{20} + \left(- 5 x^{2} - x y - \frac{y^{2}}{20}\right)$$
or
$$- 5 x^{2} + \left(- x y - y^{2}\right) = - \frac{19 y^{2}}{20} - \left(\sqrt{5} x + \frac{\sqrt{5} y}{10}\right)^{2}$$
General simplification
[src]
$$- 5 x^{2} - x y - y^{2}$$
$$- 5 x^{2} - x y - y^{2}$$
$$- 5 x^{2} - x y - y^{2}$$
Rational denominator
[src]
$$- 5 x^{2} - x y - y^{2}$$
Assemble expression
[src]
$$- 5 x^{2} - x y - y^{2}$$
$$- 5 x^{2} - x y - y^{2}$$
Combining rational expressions
[src]
$$- 5 x^{2} + y \left(- x - y\right)$$
$$- 5 x^{2} - x y - y^{2}$$