Homework Help: Solve y explicitly

1. May 8, 2010

greko

1. Solve for y explicitly , x^2-4xy+4y^2+x-12y-10=0

2. Relevant equations

3. I reduced it to (x-2y)^2=-2x+12y+10 But I have no idea how to continue.

2. May 8, 2010

Staff: Mentor

Your equation is quadratic in y. Rewrite it as 4y^2 + (stuff)y + (other stuff) = 0, and use the quadratic formula.

3. May 8, 2010

greko

Even so I cant solve for y. Can you put a step by step explanation?

4. May 8, 2010

greko

The closest I get is (y-x)^2-3y=(3x^2-x+10)/4, how can i proceed?

5. May 8, 2010

Dickfore

It is forbidden on these forums to post step-by-step solutions to a posted problem.

6. May 8, 2010

greko

sorry, I am new, but can you explain what do I do after, (y-x)^2-3y=(3x^2-x+10)/4?

7. May 8, 2010

gabbagabbahey

Start by expanding (y-x)^2...then collect terms in powers of y.

8. May 8, 2010

greko

From there, I get y^2-2xy-x^2-3y=(3x^2-x+10)/4, I guess I could complete the square on the left side but I wouldn't really get anywhere I think.

9. May 8, 2010

gabbagabbahey

When I say collect terms in powers of y, I mean write -2xy-3y as -(2x+3)y...so you have y^2-(2x+3)y-x^2=(3x^2-x+10)/4...subtract (3x^2-x+10)/4 from both sides of your equation and you can then use the quadratic equation to solve for y in terms of x.

10. May 8, 2010

greko

So would my -x^2-((3x^2-x+10)/4) be considered as my "C" value in my quadratic.

11. May 8, 2010

gabbagabbahey

yup.

12. May 8, 2010

The Chaz

So... why wouldn't we just start with:
x^2-4xy+4y^2+x-12y-10=0
(4)y^2 + (-4x-12)y +(x^2 + x -10) = 0
a, b, c....
instead of completing - then UNcompleting - the square???

13. May 8, 2010

greko

Lol, Yes i have noticed that and yes it works!. Thanks for your help guys. I just went back to my original equation and did quadratic formula =D.

14. May 8, 2010

The Chaz

Cool man. Hope to help more (or some ) in the future!

15. May 9, 2010

Staff: Mentor

Which is what I was talking about in post #2...

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