Originally Posted by

**mark** i'm looking at a worked example and it says:

a circle has equation $\displaystyle x^2 + y^2 - 8x + 10y = 0$ it says the solution involves writing the equation of the circle as $\displaystyle [x^2 - 8x] + [y^2 + 10y] = 0$ which i understand. it then goes on to talk about completing the square and makes it $\displaystyle [x^2 - 8x + (-4)^2] + [y^2 + 10y + (5)^2] = (-4)^2 + (5)^2$ and then

$\displaystyle (x - 4)^2 + (y + 5)^2 = 16 + 25$

i don't see why the $\displaystyle (-4)^2$ and the $\displaystyle (5)^2$ don't become $\displaystyle -(-4)^2$ and $\displaystyle -(5)^2$ when they've been moved to the other side of the = sign?

any help would be appreciated