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Expression simplification/ Factor perfect squares/ x^2+9*x-6

Factor x^2+9*x-6 squared

An expression to simplify:

The solution

You have entered [src] 
 2          
x  + 9*x - 6
$$\left(x^{2} + 9 x\right) - 6$$ 
x^2 + 9*x - 6
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} + 9 x\right) - 6$$
To do this, let's use the formula
$$a x^{2} + b x + c = a \left(m + x\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = 9$$
$$c = -6$$
Then
$$m = \frac{9}{2}$$
$$n = - \frac{105}{4}$$
So,
$$\left(x + \frac{9}{2}\right)^{2} - \frac{105}{4}$$
Factorization [src] 
/          _____\ /          _____\
|    9   \/ 105 | |    9   \/ 105 |
|x + - - -------|*|x + - + -------|
\    2      2   / \    2      2   /
$$\left(x + \left(\frac{9}{2} - \frac{\sqrt{105}}{2}\right)\right) \left(x + \left(\frac{9}{2} + \frac{\sqrt{105}}{2}\right)\right)$$ 
(x + 9/2 - sqrt(105)/2)*(x + 9/2 + sqrt(105)/2)
General simplification [src] 
      2      
-6 + x  + 9*x
$$x^{2} + 9 x - 6$$ 
-6 + x^2 + 9*x
Trigonometric part [src] 
      2      
-6 + x  + 9*x
$$x^{2} + 9 x - 6$$ 
-6 + x^2 + 9*x
Rational denominator [src] 
      2      
-6 + x  + 9*x
$$x^{2} + 9 x - 6$$ 
-6 + x^2 + 9*x
Common denominator [src] 
      2      
-6 + x  + 9*x
$$x^{2} + 9 x - 6$$ 
-6 + x^2 + 9*x
Assemble expression [src] 
      2      
-6 + x  + 9*x
$$x^{2} + 9 x - 6$$ 
-6 + x^2 + 9*x
Powers [src] 
      2      
-6 + x  + 9*x
$$x^{2} + 9 x - 6$$ 
-6 + x^2 + 9*x
Combining rational expressions [src] 
-6 + x*(9 + x)
$$x \left(x + 9\right) - 6$$ 
-6 + x*(9 + x)
Combinatorics [src] 
      2      
-6 + x  + 9*x
$$x^{2} + 9 x - 6$$ 
-6 + x^2 + 9*x
Numerical answer [src] 
-6.0 + x^2 + 9.0*x
-6.0 + x^2 + 9.0*x
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