PLZ HELP QUICKLY!!!!!!! Fill in the blank with a constant, so that the resulting quadratic is the square of a binomial. x^2+(4)/(5)x + \underline{~~~~}

Question

PLZ HELP QUICKLY!!!!!!!

Fill in the blank with a constant, so that the resulting quadratic is the square of a binomial.


`x^2+(4)/(5)x + \underline{~~~~}`

Answer 1

`$x^2+(4)/(5)x+(4)/(25) $`

`$\left(x+(2)/(5) \right)^2$`

Explanation:

Taking the middle coefficient:

`ax^2+bx+c`

`$c=\left((b)/(2) \right)^2$`

`$c=\left(((4)/(5) )/(2) \right)^2$`

`$c=\left((4 )/(10) \right)^2$`

`$c=\left((2 )/(5) \right)^2$`

`$c=(4)/(25) $`

Completing the square:

`$x^2+(4)/(5)x+(4)/(25) $`

`$\left(x+(2)/(5) \right)^2$`

Answer 2

To complete the square (x+2/5)^2 it would be x^2+(4/5)x+4/25