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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
$$\left(- y^{2} - y\right) + 3$$ 
-y^2 - y + 3
General simplification [src] 
         2
3 - y - y
$$- y^{2} - y + 3$$ 
3 - y - y^2
Factorization [src] 
/          ____\ /          ____\
|    1   \/ 13 | |    1   \/ 13 |
|x + - - ------|*|x + - + ------|
\    2     2   / \    2     2   /
$$\left(x + \left(\frac{1}{2} - \frac{\sqrt{13}}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{13}}{2}\right)\right)$$ 
(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
$$\left(- y^{2} - y\right) + 3$$
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
$$a = -1$$
$$b = -1$$
$$c = 3$$
Then
$$m = \frac{1}{2}$$
$$n = \frac{13}{4}$$
So,
$$\frac{13}{4} - \left(y + \frac{1}{2}\right)^{2}$$
Numerical answer [src] 
3.0 - y - y^2
3.0 - y - y^2
Common denominator [src] 
         2
3 - y - y
$$- y^{2} - y + 3$$ 
3 - y - y^2
Assemble expression [src] 
         2
3 - y - y
$$- y^{2} - y + 3$$ 
3 - y - y^2
Combining rational expressions [src] 
3 + y*(-1 - y)
$$y \left(- y - 1\right) + 3$$ 
3 + y*(-1 - y)
Trigonometric part [src] 
         2
3 - y - y
$$- y^{2} - y + 3$$ 
3 - y - y^2
Combinatorics [src] 
         2
3 - y - y
$$- y^{2} - y + 3$$ 
3 - y - y^2
Powers [src] 
         2
3 - y - y
$$- y^{2} - y + 3$$ 
3 - y - y^2
Rational denominator [src] 
         2
3 - y - y
$$- y^{2} - y + 3$$ 
3 - y - y^2
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