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Expression simplification/ Factor perfect squares/ -y^2-9*y-4

Factor -y^2-9*y-4 squared

An expression to simplify:

The solution

You have entered [src] 
   2          
- y  - 9*y - 4
$$\left(- y^{2} - 9 y\right) - 4$$ 
-y^2 - 9*y - 4
General simplification [src] 
      2      
-4 - y  - 9*y
$$- y^{2} - 9 y - 4$$ 
-4 - y^2 - 9*y
Factorization [src] 
/          ____\ /          ____\
|    9   \/ 65 | |    9   \/ 65 |
|x + - + ------|*|x + - - ------|
\    2     2   / \    2     2   /
$$\left(x + \left(\frac{9}{2} - \frac{\sqrt{65}}{2}\right)\right) \left(x + \left(\frac{\sqrt{65}}{2} + \frac{9}{2}\right)\right)$$ 
(x + 9/2 + sqrt(65)/2)*(x + 9/2 - sqrt(65)/2)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{2} - 9 y\right) - 4$$
To do this, let's use the formula
$$a y^{2} + b y + c = a \left(m + y\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = -9$$
$$c = -4$$
Then
$$m = \frac{9}{2}$$
$$n = \frac{65}{4}$$
So,
$$\frac{65}{4} - \left(y + \frac{9}{2}\right)^{2}$$
Trigonometric part [src] 
      2      
-4 - y  - 9*y
$$- y^{2} - 9 y - 4$$ 
-4 - y^2 - 9*y
Assemble expression [src] 
      2      
-4 - y  - 9*y
$$- y^{2} - 9 y - 4$$ 
-4 - y^2 - 9*y
Rational denominator [src] 
      2      
-4 - y  - 9*y
$$- y^{2} - 9 y - 4$$ 
-4 - y^2 - 9*y
Combining rational expressions [src] 
-4 + y*(-9 - y)
$$y \left(- y - 9\right) - 4$$ 
-4 + y*(-9 - y)
Powers [src] 
      2      
-4 - y  - 9*y
$$- y^{2} - 9 y - 4$$ 
-4 - y^2 - 9*y
Combinatorics [src] 
      2      
-4 - y  - 9*y
$$- y^{2} - 9 y - 4$$ 
-4 - y^2 - 9*y
Common denominator [src] 
      2      
-4 - y  - 9*y
$$- y^{2} - 9 y - 4$$ 
-4 - y^2 - 9*y
Numerical answer [src] 
-4.0 - y^2 - 9.0*y
-4.0 - y^2 - 9.0*y
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