# Thread: Can anyone show me how to complete the square on this

1. ## Can anyone show me how to complete the square on this

$\displaystyle x^2-8x+y^2+2y=-14$

2. ## Re: Can anyone show me how to complete the square on this

Originally Posted by Eraser147
$\displaystyle x^2-8x+y^2+2y=-14$
Treat the x terms and the y terms separately. Complete the square on each.

3. ## Re: Can anyone show me how to complete the square on this

It would be $\displaystyle (x-4)^2-2+(y+1)^2+13$. Which is wrong. Solutions manual says it's supposed to be $\displaystyle (x-4)^2-16+(y+1)^2-1$

4. ## Re: Can anyone show me how to complete the square on this

Remember that this is an EQUATION.

5. ## Re: Can anyone show me how to complete the square on this

so would it be what i had = 0 or = -14. I am so confused.

6. ## Re: Can anyone show me how to complete the square on this

Start with your initial equation, then whatever you add to complete the square on the x terms and the y terms, add to the other side as well, to keep the equation balanced.

7. ## Re: Can anyone show me how to complete the square on this

Can you show me? I still don't quite follow.

8. ## Re: Can anyone show me how to complete the square on this

You can show me every step you've taken, then I can guide you where you have gone wrong...

9. ## Re: Can anyone show me how to complete the square on this

okay this is what I did, I separated the x and y and completed the square for both x and y terms so I resulted in this $\displaystyle (x-4)^2-2+(y+1)^2+13$. I took $\displaystyle x^2-8x+14$ and compeleted the square first and I did the same by adding 14 on the y terms as well.

10. ## Re: Can anyone show me how to complete the square on this

Hello, Eraser147!

$\displaystyle \text{Complete the square: }\:x^2-8x+y^2+2y\:=\:\text{-}14$

We have: .$\displaystyle x^2 - 8x \qquad + y^2 + 2y \qquad \;=\;\text{-}14$

Then:. . . . $\displaystyle x^2 - 8x {\color{red}\:+\:16} + y^2 + 2y {\color{green}\:+\:1} \;=\;\text{-}14 {\color{red}\:+\:16} {\color{green}\:+\:1}$

Therefore: . . . . . .$\displaystyle (x-4)^2 + (y+1)^2 \;=\;3$

11. ## Re: Can anyone show me how to complete the square on this

Thanks Soroban, you are the best.