Instructions: Find the value of [tex]$c$[/tex] that completes the square and creates a perfect square trinomial.

[tex]
\begin{array}{l}
x^2 + 22x + c \\
c = \square
\end{array}
[/tex]



Answer :

To find the value of [tex]\( c \)[/tex] that completes the square and creates a perfect square trinomial for the expression [tex]\( x^2 + 22x + c \)[/tex], we can follow these steps:

1. Identify the coefficient of [tex]\( x \)[/tex]. In this case, the coefficient of [tex]\( x \)[/tex] is 22.

2. To complete the square, we need to take half of the coefficient of [tex]\( x \)[/tex], and then square it.

3. First, let's find half of 22:
[tex]\[ \frac{22}{2} = 11 \][/tex]

4. Next, square this result:
[tex]\[ 11^2 = 121 \][/tex]

Therefore, the value of [tex]\( c \)[/tex] that completes the square for the expression [tex]\( x^2 + 22x + c \)[/tex] is [tex]\( 121 \)[/tex].

So, [tex]\( c = 121 \)[/tex] to form the perfect square trinomial.