Use the diagram below for the expression $x^{2}+6 x+2$ to answer the following questions.
What value needs to be added to $x^{2}+6 x+2$ to complete the square?
Using your answer above, rewrite the perfect square trinomial as a squared binomial.

Step 1 ：To complete the square for the quadratic expression \(x^{2}+6 x+2\), we need to find a value \(b\) such that the expression becomes a perfect square trinomial of the form \((x+a)^2\). The coefficient of \(x\) in the expression is \(6\), so \(a\) should be \(6/2 = 3\). Therefore, the perfect square trinomial should be \((x+3)^2 = x^2 + 6x + 9\). So, the value that needs to be added to \(x^{2}+6 x+2\) to complete the square is \(9 - 2 = 7\).

Step 2 ：The value that needs to be added to \(x^{2}+6 x+2\) to complete the square is indeed 7. Now, let's rewrite the perfect square trinomial as a squared binomial. The perfect square trinomial is \((x+3)^2\).

Step 3 ：Final Answer: The value that needs to be added to \(x^{2}+6 x+2\) to complete the square is \(\boxed{7}\). The perfect square trinomial is \(\boxed{(x+3)^2}\).