# Need Help With a Quadratic Equation

1. Sep 16, 2014

### Saracen Rue

Hi, first off I want to say that I'm new here, so sorry if I do anything wrong.

Okay, now to the problem at hand. I know that this is probably really easy and I'm just having one of my moments again, but I can't for the life of me figure out how to do this question:

When the radius of a circle is increased by 6 cm, its area increases by 25%. Use the quadratic formula to find out the exact radius of the original circle.

I've spent a good 2-3 hours on it and I just can't seem to get it into the ax2+bx+c form. Any help and insight into this question you guys could provide me would be much appreciated. Thank you all for your time.

~Saracen Rue~

2. Sep 16, 2014

### Staff: Mentor

Show us what you've done.

Hint: What's the formula for the area of a circle?

3. Sep 16, 2014

### Saracen Rue

Well, the first thing I did was assign area formulas to both the original circle and the new circle, with the original one being A = πr2 and the new one being A = π(r+6)2. Now I needed to make the equations equal each other, which I did by adding 25% of the area of the first circle onto itself, giving me something that looked like this: πr2 + (25/πr2*100) = πr(r+6)2. Next, I moved the πr(r+6)2 over to the left hand side to make the equation equal to 0, allowing me to treat it as a quadratic equation. However, here's where I get stuck. I can't work out how to make it into the form ax2+bx+c.

4. Sep 16, 2014

### Staff: Mentor

Good, but you have an extra r in that right hand term. Get rid of it.

Cancel what you can cancel. Then be sure to expand that (r + 6)2 term.

5. Sep 16, 2014

### Saracen Rue

Yeah, that r was a typo.

Hm, I think my problem is that I keep getting confused with my negatives -_-
and I think I might just be tired... it is 12 in the morning where I am. I think I'll go get some sleep and try again once I'm rested. Good night.

6. Sep 16, 2014

### Staff: Mentor

Sleep is good. But you're on the right track.

7. Sep 16, 2014

### Ray Vickson

Why don't you just write $1.25 \pi r^2 = \pi (r+6)^2$? That is exactly what the question says!

8. Sep 16, 2014

### Staff: Mentor

That's just what the OP did! (Although it might not look like it.)

9. Sep 16, 2014

### Ray Vickson

Yes, I know that. But he should develop a habit of writing things more compactly. It may even be that different ways of writing correspond to different ways of thinking, so that is why I wrote what I did.

10. Sep 16, 2014

### Staff: Mentor

I certainly agree that it should be written as you wrote it.