Question

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

25
10
5
†5

Answer 1

A: 25

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* x*5+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.