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.
