math problem i need help

how would one solve
root(x-27) + root(x) = 9

so solve for x
and show steps

 

It would help if you were telling us what kind of math problem it is :/
Are you trying to expand, is it Linear equations, what?

 

just solve for x
what number does x have to be to make the equation equal to zero
Post Merge: [time]1252814348[/time]
i mean 9 not zero

 

So you're square rooting them?
As in like v/---- when it's written?

If so, x = 36

 

What is this, I don't even.

 

Sorry, I lost x at the fair yesterday. He ran away.

 

Cloudboii, your posts are not helping him at all...

zzzzzzzzzzz, here's the worked-out solution. Hopefully this helps you learn more about algebraic manipulation tricks.

Solution

EDIT (Sept. 21, 2009): Fixed link so that everyone can see it.

 

Why not, my posts gave the answer :/

You just showed an extended way of doing it, I gave him the straight out answer.

 

He was asking for steps to solve the problem. Giving just the answer only doesn't do much help to anyone.

 

Fwiw, √ is useful in this.

 

Oh, sorry >.<
Jumped into the question xD

 

root(x-27) + root(x) = 9
root(x-27) + root(x) = 9 // ^2
(x-27)^2 + x^2 = 81
x^2-729 + x^2 = 81
x^2 + X^2 = 81 + 729
2x^2 = 810
2x^2 = 810 // /2
x^2 = 405
x^2 = 405 // root
x = 20.124...
x ~ 20

I'm not sure if it's right. =P I need to check it with paper.

 

Should be (√(x-26) - √x)^2.

Hypr's already provided a thorough answer, anyway.

 

Damn, I knew I failed. XD
But it was fun to do some math problems for a long time. =P

 

Here are the steps. The trick is to move the sqrt(x) to the right, square both sides, then the x term will cancel on both sides, leaving you with just sqrt(x) and a constant.

Code:

sqrt(x-27) + sqrt(x) = 9
sqrt(x-27) = 9 - sqrt(x)
sqrt(x-27)^2 = (9 - sqrt(x))^2
x-27 = 81 - 18*sqrt(x) + sqrt(x)^2
x-27 = 81 - 18*sqrt(x) + x
-27 = 81 - 18*sqrt(x)
-108 = -18*sqrt(x)
6 = sqrt(x)
36 = x

Edit: NekoHennuli, line 3: (a+b)^2 is not the same as a^2 + b^2.

 

I worked it out and got X = 27.

 

Subbing x = 27 into the original equation gives 0 + 5.19... = 9, which is clearly incorrect.

At any rate, Hypr's already solved this (showing working as required), so this thread doesn't really have a purpose anymore.

 

It still does. I just supplied the steps to the solution (which apparently nobody figured out or were bothered enough to post...).

 

Admittedly, the steps differ slightly, but oh well.

 

Awww, people shouldn't post non-bold Solution links... I can hardly notice them...