Question

Enter the correct value so that each expression is a perfect-square trinomial.

Answer 1

To solve this problem you must apply the proccedure shown below.
 1. By definition, a perfect square trinomial has the following form:
 $a^{2}+ 2ab+b^{2}$
 2. Therefore, you must divide the middle term by 2 and square the result, as following:
 $(1/2)/2=(1/4)^{2}=1/16$
 3. As you can see, $b^{2}=1/16$, so, you can rewrite it as below:
 $(x+1/16)^{2}$
 The answer is: $1/16$

Answer 2

Answer:  The required correct value is $\dfrac{1}{16}.$

Step-by-step explanation:  We are given to find the correct value so that the following expression is a perfect square trinomial :

$E:x^2+\dfrac{1}{2}x+?$

Let the required number be represented by p.

Then, we have

$x^2+\dfrac{1}{2}x+p\\\\\\=x^2+2\times x\times \dfrac{1}{4}+\left(\dfrac{1}{4}\right)^2+p-\left(\dfrac{1}{4}\right)^2\\\\\\=\left(x+\dfrac{1}{4}\right)^2+p-\dfrac{1}{16}.$

So, to make the given expression a perfect square trinomial, we must have

$p-\dfrac{1}{16}=0\\\\\\\Rightarrow p=\dfrac{1}{16}.$

Thus, the required correct value is $\dfrac{1}{16}.$