Question

Find the number that we can place in the box, so that the resulting quadratic is the square of a binomial.

\[x^2 + \dfrac{4}{5}x + \boxed{\phantom{000}}\]

Answer 1

We need a number to complete

`(x+c)^2=x^2+2xc+c^2`

Since we have

`2xc=(4)/(5)x \iff 2c=(4)/(5)\iff c=(4)/(10)=(2)/(5)`

And so the expanded square is

`\left( x+(2)/(5)\right)^2=x^2+(4)/(5)x+(4)/(25)`