For the PrepSwift: Graphing by Completing the Square Quiz Question 2 of 2, I am a bit confused on the reversing of completing the square.

Here is the problem:

And the solution:

I understand how to get to everything up until towards the end where I highlighted. After having expanded it out, wouldn’t the “+4” that is after the “-4x” also be on the Left Hand Side (LHS) of the equation as well?

And wouldn’t you bring that “+4” over to the RHS of the equation (subtracting 4 from the “+4-5” that is on the RHS of the equation)?

using the identity : (a-b)^2 = a^2 + b^2 -2ab

To clarify on the question - I understand how completing the square yields what is on the Right Hand Side (RHS) of the equation.

But isn’t there a “+4” that also has to be added to the Left Hand Side (LHS) of the equation too since you added “+4” to the RHS?

And after that, wouldn’t the “+4” used to complete the square be brought over to the RHS as “-4”?

Please see below in green for illustration of my question.

You aren’t actually completing the square from that point; HoldMyBeer just expanded (x - 2)^2.

Oh ok, I understand now that you don’t complete the square in this instance. Thank you both!