General simplification
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$$- x^{2} + 7 x y + y^{2}$$
/ / ____\\ / / ____\\
| y*\7 - \/ 53 /| | y*\7 + \/ 53 /|
|x - --------------|*|x - --------------|
\ 2 / \ 2 /
$$\left(x - \frac{y \left(7 - \sqrt{53}\right)}{2}\right) \left(x - \frac{y \left(7 + \sqrt{53}\right)}{2}\right)$$
(x - y*(7 - sqrt(53))/2)*(x - y*(7 + sqrt(53))/2)
The perfect square
Let's highlight the perfect square of the square three-member
$$- x^{2} + \left(x 7 y + y^{2}\right)$$
Let us write down the identical expression
$$- x^{2} + \left(x 7 y + y^{2}\right) = \frac{53 y^{2}}{4} + \left(- x^{2} + 7 x y - \frac{49 y^{2}}{4}\right)$$
or
$$- x^{2} + \left(x 7 y + y^{2}\right) = \frac{53 y^{2}}{4} - \left(x - \frac{7 y}{2}\right)^{2}$$
$$- x^{2} + 7 x y + y^{2}$$
$$- x^{2} + 7 x y + y^{2}$$
$$- x^{2} + 7 x y + y^{2}$$
Rational denominator
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$$- x^{2} + 7 x y + y^{2}$$
$$- x^{2} + 7 x y + y^{2}$$
Combining rational expressions
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$$- x^{2} + y \left(7 x + y\right)$$
Assemble expression
[src]
$$- x^{2} + 7 x y + y^{2}$$