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Expression simplification/ Factor perfect squares/ -y^2-y+4

Factor -y^2-y+4 squared

An expression to simplify:

The solution

You have entered [src] 
   2        
- y  - y + 4
$$\left(- y^{2} - y\right) + 4$$ 
-y^2 - y + 4
General simplification [src] 
         2
4 - y - y
$$- y^{2} - y + 4$$ 
4 - y - y^2
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{2} - y\right) + 4$$
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
$$a = -1$$
$$b = -1$$
$$c = 4$$
Then
$$m = \frac{1}{2}$$
$$n = \frac{17}{4}$$
So,
$$\frac{17}{4} - \left(y + \frac{1}{2}\right)^{2}$$
Factorization [src] 
/          ____\ /          ____\
|    1   \/ 17 | |    1   \/ 17 |
|x + - - ------|*|x + - + ------|
\    2     2   / \    2     2   /
$$\left(x + \left(\frac{1}{2} - \frac{\sqrt{17}}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{17}}{2}\right)\right)$$ 
(x + 1/2 - sqrt(17)/2)*(x + 1/2 + sqrt(17)/2)
Numerical answer [src] 
4.0 - y - y^2
4.0 - y - y^2
Assemble expression [src] 
         2
4 - y - y
$$- y^{2} - y + 4$$ 
4 - y - y^2
Common denominator [src] 
         2
4 - y - y
$$- y^{2} - y + 4$$ 
4 - y - y^2
Rational denominator [src] 
         2
4 - y - y
$$- y^{2} - y + 4$$ 
4 - y - y^2
Powers [src] 
         2
4 - y - y
$$- y^{2} - y + 4$$ 
4 - y - y^2
Combining rational expressions [src] 
4 + y*(-1 - y)
$$y \left(- y - 1\right) + 4$$ 
4 + y*(-1 - y)
Combinatorics [src] 
         2
4 - y - y
$$- y^{2} - y + 4$$ 
4 - y - y^2
Trigonometric part [src] 
         2
4 - y - y
$$- y^{2} - y + 4$$ 
4 - y - y^2
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