Mister Exam

Factor y^2-y+7 squared

An expression to simplify:

The solution

You have entered [src]
 2        
y  - y + 7
$$\left(y^{2} - y\right) + 7$$
y^2 - y + 7
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(y^{2} - y\right) + 7$$
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
$$a = 1$$
$$b = -1$$
$$c = 7$$
Then
$$m = - \frac{1}{2}$$
$$n = \frac{27}{4}$$
So,
$$\left(y - \frac{1}{2}\right)^{2} + \frac{27}{4}$$
General simplification [src]
     2    
7 + y  - y
$$y^{2} - y + 7$$
7 + y^2 - y
Factorization [src]
/                ___\ /                ___\
|      1   3*I*\/ 3 | |      1   3*I*\/ 3 |
|x + - - + ---------|*|x + - - - ---------|
\      2       2    / \      2       2    /
$$\left(x + \left(- \frac{1}{2} - \frac{3 \sqrt{3} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} + \frac{3 \sqrt{3} i}{2}\right)\right)$$
(x - 1/2 + 3*i*sqrt(3)/2)*(x - 1/2 - 3*i*sqrt(3)/2)
Numerical answer [src]
7.0 + y^2 - y
7.0 + y^2 - y
Combinatorics [src]
     2    
7 + y  - y
$$y^{2} - y + 7$$
7 + y^2 - y
Trigonometric part [src]
     2    
7 + y  - y
$$y^{2} - y + 7$$
7 + y^2 - y
Powers [src]
     2    
7 + y  - y
$$y^{2} - y + 7$$
7 + y^2 - y
Combining rational expressions [src]
7 + y*(-1 + y)
$$y \left(y - 1\right) + 7$$
7 + y*(-1 + y)
Common denominator [src]
     2    
7 + y  - y
$$y^{2} - y + 7$$
7 + y^2 - y
Assemble expression [src]
     2    
7 + y  - y
$$y^{2} - y + 7$$
7 + y^2 - y
Rational denominator [src]
     2    
7 + y  - y
$$y^{2} - y + 7$$
7 + y^2 - y