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Expression simplification/ Factor perfect squares/ -y^2-y-5

Factor -y^2-y-5 squared

An expression to simplify:

The solution

You have entered [src] 
   2        
- y  - y - 5
$$\left(- y^{2} - y\right) - 5$$ 
-y^2 - y - 5
General simplification [src] 
          2
-5 - y - y
$$- y^{2} - y - 5$$ 
-5 - y - y^2
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{2} - y\right) - 5$$
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
$$a = -1$$
$$b = -1$$
$$c = -5$$
Then
$$m = \frac{1}{2}$$
$$n = - \frac{19}{4}$$
So,
$$- \left(y + \frac{1}{2}\right)^{2} - \frac{19}{4}$$
Factorization [src] 
/            ____\ /            ____\
|    1   I*\/ 19 | |    1   I*\/ 19 |
|x + - + --------|*|x + - - --------|
\    2      2    / \    2      2    /
$$\left(x + \left(\frac{1}{2} - \frac{\sqrt{19} i}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{19} i}{2}\right)\right)$$ 
(x + 1/2 + i*sqrt(19)/2)*(x + 1/2 - i*sqrt(19)/2)
Trigonometric part [src] 
          2
-5 - y - y
$$- y^{2} - y - 5$$ 
-5 - y - y^2
Powers [src] 
          2
-5 - y - y
$$- y^{2} - y - 5$$ 
-5 - y - y^2
Rational denominator [src] 
          2
-5 - y - y
$$- y^{2} - y - 5$$ 
-5 - y - y^2
Assemble expression [src] 
          2
-5 - y - y
$$- y^{2} - y - 5$$ 
-5 - y - y^2
Numerical answer [src] 
-5.0 - y - y^2
-5.0 - y - y^2
Combinatorics [src] 
          2
-5 - y - y
$$- y^{2} - y - 5$$ 
-5 - y - y^2
Combining rational expressions [src] 
-5 + y*(-1 - y)
$$y \left(- y - 1\right) - 5$$ 
-5 + y*(-1 - y)
Common denominator [src] 
          2
-5 - y - y
$$- y^{2} - y - 5$$ 
-5 - y - y^2
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