Express x^2-4x+9 in the form (x-p)^2+q where p and q are integers

The first step would be to expand the second equation:(x-p)^2+qx^2-px-px+p^2+q

this simplifies to x^2-2px+p^2+q

After this you examine the two equations and identify their similarities such as the x^2 term and the terms with have a single x in them.

From this you can equate the terms which have similar terms (see below)

-2px=-4x and p^2+q=9

Next determine which equation is solvable.

As -2px=-4x only has one variable is it solvable.

Solving this equations gives:

-2px=-4x

cancelling x

-2p=-4

divide both sides by -2

p=2 (save this)

Next use this solution to solve the second equation:

p^2+q=9

substitute p=2

2^2+q=94+q=9

q=5 (save this)

Finally substitute the values for p and q into the original equation

 (x-p)^2+q

 final answer: (x-2)^2+5

This can be checked by expanding it and ensuring that it does become x^2-4x+9.