1. ## Center and radius of circle.

Alright so it says find the center and radius of THIS :

$\displaystyle x^2 + y^2 + x = 0$

Somehow they got numbers that WERENT variables in there

(Moved the x's together and put them in brackets) Like this :

$\displaystyle (x^2 + x) + y^2$

(Then put these in)

$\displaystyle (x^2 + x + {1\over 4} - {1\over 4}) + y^2$

What the HELL did they do to be able to do that? Like it cancels out so can i put whatever numbers i want in there as long as they equal 0 or something? In that case wouldnt using 1 make it easier?

Any explainations?

Can post next steps of the answer if anyone would like

2. It's called completing the square. You need to have the form of (x-h)^2+(y-k)^2=r^2 for a circle. When you have unfactored variables, you have to get it into a form that does factor.

As long as the coefficient in front of the squared power (x^2 or y^2) is one, you take the coefficient in front of the x or y term, divide by 2 then square that. For your problem the coefficient was 1, divided by 2 is 1/2, and squared is 1/4. Since you added 1/4 you must also subtract it to keep equality. But now the x terms factor to (x+1/2)^2.

It just takes practice. It's not a hard operation.