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Question 1 of 10

What value of [tex]$c$[/tex] will complete the square in the expression below and make the expression a perfect square trinomial?

[tex]x^2 + 16x + c[/tex]

Enter the perfect square trinomial as a squared binomial.


Sagot :

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].