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Expression simplification/ Factor perfect squares/ x^2-100*x+5000

Factor x^2-100*x+5000 squared

An expression to simplify:

The solution

You have entered [src] 
 2               
x  - 100*x + 5000
$$\left(x^{2} - 100 x\right) + 5000$$ 
x^2 - 100*x + 5000
General simplification [src] 
        2        
5000 + x  - 100*x
$$x^{2} - 100 x + 5000$$ 
5000 + x^2 - 100*x
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} - 100 x\right) + 5000$$
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
$$a = 1$$
$$b = -100$$
$$c = 5000$$
Then
$$m = -50$$
$$n = 2500$$
So,
$$\left(x - 50\right)^{2} + 2500$$
Factorization [src] 
(x + -50 + 50*I)*(x + -50 - 50*I)
$$\left(x + \left(-50 - 50 i\right)\right) \left(x + \left(-50 + 50 i\right)\right)$$ 
(x - 50 + 50*i)*(x - 50 - 50*i)
Rational denominator [src] 
        2        
5000 + x  - 100*x
$$x^{2} - 100 x + 5000$$ 
5000 + x^2 - 100*x
Combinatorics [src] 
        2        
5000 + x  - 100*x
$$x^{2} - 100 x + 5000$$ 
5000 + x^2 - 100*x
Numerical answer [src] 
5000.0 + x^2 - 100.0*x
5000.0 + x^2 - 100.0*x
Powers [src] 
        2        
5000 + x  - 100*x
$$x^{2} - 100 x + 5000$$ 
5000 + x^2 - 100*x
Trigonometric part [src] 
        2        
5000 + x  - 100*x
$$x^{2} - 100 x + 5000$$ 
5000 + x^2 - 100*x
Common denominator [src] 
        2        
5000 + x  - 100*x
$$x^{2} - 100 x + 5000$$ 
5000 + x^2 - 100*x
Combining rational expressions [src] 
5000 + x*(-100 + x)
$$x \left(x - 100\right) + 5000$$ 
5000 + x*(-100 + x)
Assemble expression [src] 
        2        
5000 + x  - 100*x
$$x^{2} - 100 x + 5000$$ 
5000 + x^2 - 100*x
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