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Expression simplification/ Factor perfect squares/ -a^2-a+8

Factor -a^2-a+8 squared

An expression to simplify:

The solution

You have entered [src] 
   2        
- a  - a + 8
(−a2−a)+8\left(- a^{2} - a\right) + 8 
-a^2 - a + 8
Factorization [src] 
/          ____\ /          ____\
|    1   \/ 33 | |    1   \/ 33 |
|a + - - ------|*|a + - + ------|
\    2     2   / \    2     2   /
(a+(12−332))(a+(12+332))\left(a + \left(\frac{1}{2} - \frac{\sqrt{33}}{2}\right)\right) \left(a + \left(\frac{1}{2} + \frac{\sqrt{33}}{2}\right)\right) 
(a + 1/2 - sqrt(33)/2)*(a + 1/2 + sqrt(33)/2)
General simplification [src] 
         2
8 - a - a
−a2−a+8- a^{2} - a + 8 
8 - a - a^2
The perfect square
Let's highlight the perfect square of the square three-member
(−a2−a)+8\left(- a^{2} - a\right) + 8
To do this, let's use the formula
a3+ab+c=a(a+m)2+na^{3} + a b + c = a \left(a + m\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=8c = 8
Then
m=12m = \frac{1}{2}
n=334n = \frac{33}{4}
So,
88
Common denominator [src] 
         2
8 - a - a
−a2−a+8- a^{2} - a + 8 
8 - a - a^2
Rational denominator [src] 
         2
8 - a - a
−a2−a+8- a^{2} - a + 8 
8 - a - a^2
Trigonometric part [src] 
         2
8 - a - a
−a2−a+8- a^{2} - a + 8 
8 - a - a^2
Assemble expression [src] 
         2
8 - a - a
−a2−a+8- a^{2} - a + 8 
8 - a - a^2
Combining rational expressions [src] 
8 + a*(-1 - a)
a(−a−1)+8a \left(- a - 1\right) + 8 
8 + a*(-1 - a)
Powers [src] 
         2
8 - a - a
−a2−a+8- a^{2} - a + 8 
8 - a - a^2
Combinatorics [src] 
         2
8 - a - a
−a2−a+8- a^{2} - a + 8 
8 - a - a^2
Numerical answer [src] 
8.0 - a - a^2
8.0 - a - a^2
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