Write x^2-4x+9 in the form (x-p)^2+q, where p and q are integers.
To complete this task we use a method called "Completing the square. For this we use a formula (a+b)^2=a^2+2ab+b^2.
Now we see that in the example we have a term x^2 so we put x^2=a^2 so we can have that x=a. Then -4x=2ab=2xb so b=-2. Then (x-2)^2=x^2-4x+4. In order to substitute this in the place of x^2-4x, we have to subtract -4. Then we have x^2-4x+9=(x-2)^2-4+9=(x-2)^2+5 which is in the required form (x-p)^2+q where p=2 and q=5.
MS
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