well... for one... you can't pull out the squares like he did in step 3 since 45 isn't a square number, also, even taking that into consideration, when the squares were pulled out, you also removed the 6 from the equation entirely as well as the square root number of 45, so it's an entirely false and wrong problem.

Actually the math was valid up until step 4. (4-9/2)*(4-9/2) = 16-36+81/4 and same for the other side. He just completed the square.

It's still just mucking up the math equation, and regardless... it comes out wrong

The error lies in the fourth step. In order to simplify (4-9/2)^2 = (5-9/2)^2
you would need to square root both sides, making the equation |4-9/2| = |5-9/2|
which simplifies to |-.5| = |.5| which is .5 = .5

MATH

too lazy to find the error in it..