Question

Which constant term should be used to complete the square

Answer 1

`(25)/(4)`

1) We can complete the square, by picking the coefficient b and dividing by 2. In this case:

`\begin{gathered} b=5 \\ (5)/(2) \end{gathered}`

2) So, now we can proceed with that reminding ourselves that any number added to the left side must be added to the right side so that the equation remains true.

Let's pick that 5/2 and square it:

`((5)/(2))^2=(25)/(4)`

So now, we can write out:

`\begin{gathered} x^2-5x+(25)/(4)=7+(25)/(4) \\ (x-(5)/(2))^2=(53)/(4) \end{gathered}`

Thus, the number to be added is 25/4