To solve the given equation [tex]\( x^2 - 18x + \ldots = 4 + \ldots \)[/tex] by completing the square, follow these steps:
1. Identify the coefficient of [tex]\( x \)[/tex]:
- The coefficient of [tex]\( x \)[/tex] in the equation [tex]\( x^2 - 18x + \ldots \)[/tex] is [tex]\(-18\)[/tex].
2. Find half of this coefficient:
- Half of [tex]\(-18\)[/tex] is [tex]\(\frac{-18}{2} = -9\)[/tex].
3. Square the result from step 2:
- Squaring [tex]\(-9\)[/tex] gives [tex]\( (-9)^2 = 81 \)[/tex].
To complete the square, you need to add [tex]\( 81 \)[/tex] to both sides of the equation.
So, the correct number to fill in the blanks for the first step of completing the square is:
[tex]\[
x^2 - 18x + 81 = 4 + 81
\][/tex]
Therefore, the correct answer is B. 81.
