Question

Which of the following values "completes the square," or creates a perfect square trinomial, for x2 + 10x +_

Answer 1

Answer:

A: 25

Step-by-step explanation:

Take 10, since it's the middle number, divide it in half, and then square it. Your answer is then 25

Answer 2

Answer:  The correct option is

(A) 25.

Step-by-step explanation:  We are given to select the value that completes the square or creates a perfect square trinomial from the following :

$E=x^2+10x+?$

We will be using the following formula :

$(a+b)^2=a^2+2ab+b^2.$

Let c represents the required value that completes the square.

Then, we have

$E\\\\=x^2+10x+c\\\\=(x^2+2\times x\times5+5^2)+c-5^2\\\\=(x+5)^2+c-25.$

So, if E is a perfect square trinomial, then we must have

$c-25=0\\\\\Rightarrow c=25.$

Thus, the required value is 25.

Option (A) is CORRECT.