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Expression simplification/ Factor perfect squares/ 9*b^2-7*b-3

Factor 9*b^2-7*b-3 squared

An expression to simplify:

The solution

You have entered [src] 
   2          
9*b  - 7*b - 3
$$\left(9 b^{2} - 7 b\right) - 3$$ 
9*b^2 - 7*b - 3
Factorization [src] 
/             _____\ /             _____\
|      7    \/ 157 | |      7    \/ 157 |
|b + - -- + -------|*|b + - -- - -------|
\      18      18  / \      18      18  /
$$\left(b + \left(- \frac{7}{18} + \frac{\sqrt{157}}{18}\right)\right) \left(b + \left(- \frac{\sqrt{157}}{18} - \frac{7}{18}\right)\right)$$ 
(b - 7/18 + sqrt(157)/18)*(b - 7/18 - sqrt(157)/18)
General simplification [src] 
              2
-3 - 7*b + 9*b
$$9 b^{2} - 7 b - 3$$ 
-3 - 7*b + 9*b^2
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(9 b^{2} - 7 b\right) - 3$$
To do this, let's use the formula
$$a b^{2} + b^{2} + c = a \left(b + m\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 9$$
$$b = -7$$
$$c = -3$$
Then
$$m = - \frac{7}{18}$$
$$n = - \frac{157}{36}$$
So,
$$9 \left(b - \frac{7}{18}\right)^{2} - \frac{157}{36}$$
Numerical answer [src] 
-3.0 + 9.0*b^2 - 7.0*b
-3.0 + 9.0*b^2 - 7.0*b
Assemble expression [src] 
              2
-3 - 7*b + 9*b
$$9 b^{2} - 7 b - 3$$ 
-3 - 7*b + 9*b^2
Common denominator [src] 
              2
-3 - 7*b + 9*b
$$9 b^{2} - 7 b - 3$$ 
-3 - 7*b + 9*b^2
Trigonometric part [src] 
              2
-3 - 7*b + 9*b
$$9 b^{2} - 7 b - 3$$ 
-3 - 7*b + 9*b^2
Rational denominator [src] 
              2
-3 - 7*b + 9*b
$$9 b^{2} - 7 b - 3$$ 
-3 - 7*b + 9*b^2
Combining rational expressions [src] 
-3 + b*(-7 + 9*b)
$$b \left(9 b - 7\right) - 3$$ 
-3 + b*(-7 + 9*b)
Combinatorics [src] 
              2
-3 - 7*b + 9*b
$$9 b^{2} - 7 b - 3$$ 
-3 - 7*b + 9*b^2
Powers [src] 
              2
-3 - 7*b + 9*b
$$9 b^{2} - 7 b - 3$$ 
-3 - 7*b + 9*b^2
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