Question

Fill in the blanks so the left side is a perfect square trinomial. That is, complete the square.x² + 8/9x+__ = (x+__)^2

Answer 1

Given:

There are given the equation:

`x^2+(8)/(9)x+()=(x+())^2`

Step-by-step explanation:

According to the question:

We need to find the missing terms:

So,

From the equation:

`(x+(4)/(9))^2=x^2+(2.x.4)/(9)+((4)/(9))^2`

Then,

`\begin{gathered} (x+(4)/(9))^2=x^2+(2.x.4)/(9)+((4)/(9))^2 \\ =x^2+(8x)/(9)+(16)/(81) \\ =x^2+(8)/(9)x+(16)/(81) \end{gathered}`

Final answer:

Hence, the missing value is shown below:

`x^2+(8)/(9)x+(16)/(81)=(x+(4)/(9))^2`