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Expression simplification/ Factor perfect squares/ -y^2-7*y*x-x^2

Factor -y^2-7*y*x-x^2 squared

An expression to simplify:

The solution

You have entered [src] 
   2            2
- y  - 7*y*x - x
$$- x^{2} + \left(- x 7 y - y^{2}\right)$$ 
-y^2 - 7*y*x - x^2
General simplification [src] 
   2    2        
- x  - y  - 7*x*y
$$- x^{2} - 7 x y - y^{2}$$ 
-x^2 - y^2 - 7*x*y
Factorization [src] 
/      /         ___\\ /      /        ___\\
|    y*\-7 + 3*\/ 5 /| |    y*\7 + 3*\/ 5 /|
|x - ----------------|*|x + ---------------|
\           2        / \           2       /
$$\left(x - \frac{y \left(-7 + 3 \sqrt{5}\right)}{2}\right) \left(x + \frac{y \left(3 \sqrt{5} + 7\right)}{2}\right)$$ 
(x - y*(-7 + 3*sqrt(5))/2)*(x + y*(7 + 3*sqrt(5))/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
$$- x^{2} + \left(- x 7 y - y^{2}\right) = \frac{45 y^{2}}{4} + \left(- x^{2} - 7 x y - \frac{49 y^{2}}{4}\right)$$
or
$$- x^{2} + \left(- x 7 y - y^{2}\right) = \frac{45 y^{2}}{4} - \left(x + \frac{7 y}{2}\right)^{2}$$
Rational denominator [src] 
   2    2        
- x  - y  - 7*x*y
$$- x^{2} - 7 x y - y^{2}$$ 
-x^2 - y^2 - 7*x*y
Assemble expression [src] 
   2    2        
- x  - y  - 7*x*y
$$- x^{2} - 7 x y - y^{2}$$ 
-x^2 - y^2 - 7*x*y
Trigonometric part [src] 
   2    2        
- x  - y  - 7*x*y
$$- x^{2} - 7 x y - y^{2}$$ 
-x^2 - y^2 - 7*x*y
Combinatorics [src] 
   2    2        
- x  - y  - 7*x*y
$$- x^{2} - 7 x y - y^{2}$$ 
-x^2 - y^2 - 7*x*y
Powers [src] 
   2    2        
- x  - y  - 7*x*y
$$- x^{2} - 7 x y - y^{2}$$ 
-x^2 - y^2 - 7*x*y
Common denominator [src] 
   2    2        
- x  - y  - 7*x*y
$$- x^{2} - 7 x y - y^{2}$$ 
-x^2 - y^2 - 7*x*y
Combining rational expressions [src] 
   2               
- x  + y*(-y - 7*x)
$$- x^{2} + y \left(- 7 x - y\right)$$ 
-x^2 + y*(-y - 7*x)
Numerical answer [src] 
-x^2 - y^2 - 7.0*x*y
-x^2 - y^2 - 7.0*x*y
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