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Expression simplification/ Factor perfect squares/ t^2+5*t*x+x^2

Factor t^2+5*t*x+x^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2            2
t  + 5*t*x + x
$$x^{2} + \left(t^{2} + 5 t x\right)$$ 
t^2 + (5*t)*x + x^2
The perfect square
Let's highlight the perfect square of the square three-member
$$x^{2} + \left(t^{2} + 5 t x\right)$$
Let us write down the identical expression
$$x^{2} + \left(t^{2} + 5 t x\right) = - \frac{21 x^{2}}{4} + \left(t^{2} + 5 t x + \frac{25 x^{2}}{4}\right)$$
or
$$x^{2} + \left(t^{2} + 5 t x\right) = - \frac{21 x^{2}}{4} + \left(t + \frac{5 x}{2}\right)^{2}$$
in the view of the product
$$\left(- \sqrt{\frac{21}{4}} x + \left(t + \frac{5 x}{2}\right)\right) \left(\sqrt{\frac{21}{4}} x + \left(t + \frac{5 x}{2}\right)\right)$$
$$\left(- \frac{\sqrt{21}}{2} x + \left(t + \frac{5 x}{2}\right)\right) \left(\frac{\sqrt{21}}{2} x + \left(t + \frac{5 x}{2}\right)\right)$$
$$\left(t + x \left(\frac{5}{2} - \frac{\sqrt{21}}{2}\right)\right) \left(t + x \left(\frac{\sqrt{21}}{2} + \frac{5}{2}\right)\right)$$
$$\left(t + x \left(\frac{5}{2} - \frac{\sqrt{21}}{2}\right)\right) \left(t + x \left(\frac{\sqrt{21}}{2} + \frac{5}{2}\right)\right)$$
General simplification [src] 
 2    2        
t  + x  + 5*t*x
$$t^{2} + 5 t x + x^{2}$$ 
t^2 + x^2 + 5*t*x
Factorization [src] 
/      /       ____\\ /      /      ____\\
|    x*\-5 + \/ 21 /| |    x*\5 + \/ 21 /|
|t - ---------------|*|t + --------------|
\           2       / \          2       /
$$\left(t - \frac{x \left(-5 + \sqrt{21}\right)}{2}\right) \left(t + \frac{x \left(\sqrt{21} + 5\right)}{2}\right)$$ 
(t - x*(-5 + sqrt(21))/2)*(t + x*(5 + sqrt(21))/2)
Numerical answer [src] 
t^2 + x^2 + 5.0*t*x
t^2 + x^2 + 5.0*t*x
Combinatorics [src] 
 2    2        
t  + x  + 5*t*x
$$t^{2} + 5 t x + x^{2}$$ 
t^2 + x^2 + 5*t*x
Common denominator [src] 
 2    2        
t  + x  + 5*t*x
$$t^{2} + 5 t x + x^{2}$$ 
t^2 + x^2 + 5*t*x
Trigonometric part [src] 
 2    2        
t  + x  + 5*t*x
$$t^{2} + 5 t x + x^{2}$$ 
t^2 + x^2 + 5*t*x
Combining rational expressions [src] 
 2              
x  + t*(t + 5*x)
$$t \left(t + 5 x\right) + x^{2}$$ 
x^2 + t*(t + 5*x)
Powers [src] 
 2    2        
t  + x  + 5*t*x
$$t^{2} + 5 t x + x^{2}$$ 
t^2 + x^2 + 5*t*x
Assemble expression [src] 
 2    2        
t  + x  + 5*t*x
$$t^{2} + 5 t x + x^{2}$$ 
t^2 + x^2 + 5*t*x
Rational denominator [src] 
 2    2        
t  + x  + 5*t*x
$$t^{2} + 5 t x + x^{2}$$ 
t^2 + x^2 + 5*t*x
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