To complete the square in the expression [tex]\( x^2 + 16x + c \)[/tex], follow these steps:
1. Identify the coefficient of [tex]\( x \)[/tex]:
The coefficient of [tex]\( x \)[/tex] in the expression [tex]\( x^2 + 16x + c \)[/tex] is 16.
2. Divide the coefficient of [tex]\( x \)[/tex] by 2:
Calculate [tex]\( \frac{16}{2} \)[/tex]:
[tex]\[
\frac{16}{2} = 8
\][/tex]
3. Square the result from step 2:
Compute [tex]\( 8^2 \)[/tex]:
[tex]\[
8^2 = 64
\][/tex]
Therefore, the value of [tex]\( c \)[/tex] that will complete the square is 64.
4. Form the perfect square trinomial:
The given expression [tex]\( x^2 + 16x + 64 \)[/tex] can now be written as a perfect square trinomial.
5. Write the expression as a squared binomial:
The squared binomial form is:
[tex]\[
(x + 8)^2
\][/tex]
So, the value of [tex]\( c \)[/tex] that completes the square is 64, and the perfect square trinomial can be expressed as [tex]\( (x + 8)^2 \)[/tex].
