Question

Solve:
square root of (x+6) + square root of (x) = 2

Answer 1

√(x+6) + √x = 2
Square both sides:
(x+6) + 2√(x^2+6x) + x = 4
Do you see how I got that?

Answer 2

No, I was taught to move the 2nd radical over and not work with it until I got the first one out of the way. My second line reads: (x+6)=4-4(square root of x) + x

Answer 3

Oh. That's probably a better method.
Now move your new radical over to the other side and all the other terms onto the opposite side, and square again.

Answer 4

I get 16x=4; x= 1/4. How do I put that fraction back into the original problem to check it? My answer was 1/4, but it got counted wrong. So either I did something wrong or there is no real solution.

Answer 5

√(1/4 + 6) + √1/4 = 2.
Just plug in the 1/4.
Now, does that work?

Answer 6

That is the point where I don't know how to calculate that fraction under the square root

Answer 7

√1/4 = √1 / √4 = 1/2.
That makes sense because (1/2) ^2 = 1/4.

Answer 8

Yes, I see that, but the answer of 1/4 is wrong.

Answer 9

Yes. So maybe your original answer is wrong.
1. Maybe there was a wrong calculation somewhere...
2. Or maybe you were right and there is no real solution.
Try checking your work and trying again.

Answer 10

I've checked several times. That's why I was posting to see if someone could tell me why that 1/4 was wrong if I was working the problem correctly.

Answer 11

If you've checked, I guess you were right. There is no real solution.

Answer 12

That equation looked fishy from the start...

Answer 13

Thanks!

Answer 14

No problem. :)