Question

What constant term should be used to complete the square? x 2 - 5x + _____ = 7

Answer 1

`c=(25)/(4)`

Explanation:

The given equation is:

`x^2-5x+--=7`

Rewriting the above given equations, we have

`x^2-5x+c=7` where c is the constant term that is used to complete the square.

Now, In order to get the constant term c, we use the formula that is

`c=((-b)/(2a))^2`

where
`a=1` and
`b=-5`

Substituting these values, we have

`c=((-(-5))/(2(1)))^2`

`c=((5)/(2))^2`

`c=(25)/(4)`

Thus,
`c=(25)/(4)` is the constant term that is used to complete the square.

Answer 2

Given x^2-5x+c=7, the constant term c will be obtained using the formula:
c=(-b/2a)²
given that a=1 and b=-5 then plugging the values we shall have:
c=(-(-5)/2*1)²
c=(5/2)²
c=25/4

Answer: the constant is 25/4