Rewrite x^2-2x+8y + 25=0 in the form (x-h)^2=4p(y-k)

Question

anonymous · Answer

Please help!

paxpolaris · Answer

$$x^2-2x+8y + 25=0 $$$$\implies x^2-2x=-8y - 25$$$$\implies x^2-2x+1=-8y - 25+1$$$$\implies \left(  x-1 \right)^2=-8y - 24$$$$\implies \left(  x-1 \right)^2=-8(y +3)$$

paxpolaris · Answer

$$\huge\implies \left(  x-1 \right)^2=4 \cdot (-2)\left[y-\left( -3 \right)\right]$$

anonymous · Answer

Okay thank you. How can I decide what to do? I mean I never know what steps to take?

paxpolaris · Answer

First move all the x terms on one side & all the non-x terms on the other... 

Then you need to add to both sides a number that would make the x side a perfect square. 
Generally if you have x^2+ bx  you would add: $$\left( \frac b2 \right)^2 or\  {b^2 \over 4}$$