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The equation can be solved by completing the square. What number should go in the blanks for the first step?

[tex]\[ x^2 - 18x + \ldots = 4 + \ldots \][/tex]

A. 324
B. 81
C. 9
D. 18

Sagot :

GinnyAnswer
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.
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