Answer:
9 should be added to the expression to make it a perfect square
Step-by-step explanation:
Given expression:
[tex]w^2-6w+_-[/tex]
To fill in the missing term such that the expression becomes a perfect square.
Solution:
In order to make the expression a perfect square we will use completing the square method.
We have : [tex]w^2-6w[/tex]
By complete the square method we will add the square of the quotient of the co-efficient of the middle term which is [tex]-6w[/tex] and 2.
The co-efficient of middle term = -6
Thus the number to be added will be = [tex](\frac{-6}{2})^2=(-3)^2=9[/tex]
Thus, on adding 9 the expression will become:
[tex]w^2-6w+9[/tex] which is a perfect square of the binomial [tex](w-3)[/tex]
This can be shown as:
[tex](w-3)^2=w^2-6w+9[/tex]
Thus, we add 9 to the expression to make it a perfect square.
Answer:
9
Step-by-step explanation:
Given: [tex]w^{2} -6w+[/tex]
Finding the number to make expression a perfect square.
From the expression we can see that coefficient of variable is 1 and -6.
Now, lets take a= 1 and b= -6 and finding c .
∴ c= [tex]\frac{b^{2} }{4a}[/tex]
Subtituting the value of a and b.
⇒ c= [tex]\frac{-6^{2} }{4\times 1} = \frac{36}{4}[/tex] (∵ [tex]-6\times -6= 36[/tex])
∴ c= 9
Next putting the value in the expression.
[tex]w^{2} -6w+9[/tex]
= [tex](w-3)(w-3)[/tex]
= [tex](w-3)^{2}[/tex]
Hence, 9 is a number to make the expression a perfect square.
