contestada

Find the number that we can place in the box, so that the resulting quadratic is the square of a binomial.
\[x^2 + \dfrac{4}{5}x + \boxed{\phantom{000}}\]

Respuesta :

We need a number to complete

[tex](x+c)^2=x^2+2xc+c^2[/tex]

Since we have

[tex]2xc=\dfrac{4}{5}x \iff 2c=\dfrac{4}{5}\iff c=\dfrac{4}{10}=\dfrac{2}{5}[/tex]

And so the expanded square is

[tex]\left( x+\dfrac{2}{5}\right)^2=x^2+\dfrac{4}{5}x+\dfrac{4}{25}[/tex]

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