How to simplify without using the abc formula

Question

I usually use abc formula to simplify expressions. I'm simplifying $x^2-6x+10$. Using the abc formula I get a complex solution. I checked the answer and found theres a much simpler way to write it. How can I see that $x^2-6x+10 =(x-3)^2 +1$? Now that I have seen the answer I know it totally makes sense. But I want to see it before checking the answer.

Answer 1

$(x-a)^2=x^2-2a+a^2$, so if you have $x^2-bx+c$, it is $\left(x-\dfrac b2\right)^2+c-\left(\dfrac b2\right)^2.$