Answer:
[tex]$x^2+\frac{4}{5}x+\frac{4}{25} $[/tex]
[tex]$\left(x+\frac{2}{5} \right)^2$[/tex]
Step-by-step explanation:
Taking the middle coefficient:
[tex]ax^2+bx+c[/tex]
[tex]$c=\left(\frac{b}{2} \right)^2$[/tex]
[tex]$c=\left(\frac{\frac{4}{5} }{2} \right)^2$[/tex]
[tex]$c=\left(\frac{4 }{10} \right)^2$[/tex]
[tex]$c=\left(\frac{2 }{5} \right)^2$[/tex]
[tex]$c=\frac{4}{25} $[/tex]
Completing the square:
[tex]$x^2+\frac{4}{5}x+\frac{4}{25} $[/tex]
[tex]$\left(x+\frac{2}{5} \right)^2$[/tex]
