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Expression simplification/ Factor perfect squares/ -y^2-y+3

Factor -y^2-y+3 squared

An expression to simplify:

The solution

You have entered [src] 
   2        
- y  - y + 3
(−y2−y)+3\left(- y^{2} - y\right) + 3 
-y^2 - y + 3
General simplification [src] 
         2
3 - y - y
−y2−y+3- y^{2} - y + 3 
3 - y - y^2
Factorization [src] 
/          ____\ /          ____\
|    1   \/ 13 | |    1   \/ 13 |
|x + - - ------|*|x + - + ------|
\    2     2   / \    2     2   /
(x+(12−132))(x+(12+132))\left(x + \left(\frac{1}{2} - \frac{\sqrt{13}}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{13}}{2}\right)\right) 
(x + 1/2 - sqrt(13)/2)*(x + 1/2 + sqrt(13)/2)
The perfect square
Let's highlight the perfect square of the square three-member
(−y2−y)+3\left(- y^{2} - y\right) + 3
To do this, let's use the formula
ay2+by+c=a(m+y)2+na y^{2} + b y + c = a \left(m + y\right)^{2} + n
where
m=b2am = \frac{b}{2 a}
n=4ac−b24an = \frac{4 a c - b^{2}}{4 a}
In this case
a=−1a = -1
b=−1b = -1
c=3c = 3
Then
m=12m = \frac{1}{2}
n=134n = \frac{13}{4}
So,
134−(y+12)2\frac{13}{4} - \left(y + \frac{1}{2}\right)^{2}
Numerical answer [src] 
3.0 - y - y^2
3.0 - y - y^2
Common denominator [src] 
         2
3 - y - y
−y2−y+3- y^{2} - y + 3 
3 - y - y^2
Assemble expression [src] 
         2
3 - y - y
−y2−y+3- y^{2} - y + 3 
3 - y - y^2
Combining rational expressions [src] 
3 + y*(-1 - y)
y(−y−1)+3y \left(- y - 1\right) + 3 
3 + y*(-1 - y)
Trigonometric part [src] 
         2
3 - y - y
−y2−y+3- y^{2} - y + 3 
3 - y - y^2
Combinatorics [src] 
         2
3 - y - y
−y2−y+3- y^{2} - y + 3 
3 - y - y^2
Powers [src] 
         2
3 - y - y
−y2−y+3- y^{2} - y + 3 
3 - y - y^2
Rational denominator [src] 
         2
3 - y - y
−y2−y+3- y^{2} - y + 3 
3 - y - y^2
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