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what I think you should do is first multiply the (x-1) by (x^2-4)

then square both sides, and then collect the like terms

How do I multiply (x-1) by (x^2-4)?

expand the brackets

Is it x^3-x^2-4x+4?

yea

Yay. :D Then how do I combine like terms?

you have to square both sides first, then collect the like terms, then isolate x

there might be an easier way, but i'm not sure

Square both sides? How?

to get rid of the sqrt sign, you'll need to square both sides:
\[(x^3-x^2-4x+4)^2=x^4-2x^3\]

Wait, wouldn't it be (x^4-2x^3)^2 on that side?

Oh I get it.

Do I have to do the (x^3-x^2-4x+4)^2 first?

yes, now it's a very, very, very long process. Are you allowed to use a calculator for this part?

Yes I am.

so type \[(x^3 −x^2 −4x+4)^2\] into the calculator to get an answer

How do I do that if I'm using the google calculator?

I've never used a google calc. let me see

The calculator I normally use is broken, sorry. :(

Alright I got it. What next?

subtract x^4 from both sides and add 2x^3 to get one side equal to 0

Alright, now I can do x^2-x^2 to get -, correct?

to get 0*

how'd you get x^2?

but, yes, use that idea to get all the terms on one side

x^6-x^4=x^2 and -2x^5+2x^3=x^2, right?

no, you can't do that. they're not like terms. like terms are:
x and 4x
x^2 and 7x^2
not x^6 and x^4

so what you should have gotten is: \[x^6-2x^5-7x^4+16x^3+8x^2-32x+16=x^4+2x^3\]

Mind if I make a suggestion that will keep things simpler?

@whpalmer4 of course @Chelsea04 Wouldn't it be =x^4-2x^3?

oh, yes sorry.

yea, but how does that help? I noticed it too, but didn't know what to do with it

then what?

we marvel at how beautiful it is? :-)

wouldn't you have to eventually expand it to solve for x?
@whpalmer4 that's funny, lol :P

If we expand it out, we get
\[x^5-8x^3+2x^2+12x-8=0\]

I am just so confused right now.

what exactly does the question ask?

It just says solve.

I guess you could've just typed the whole thing into the calculator

Now here's a thought, what if the problem is really
\[x-1 = \sqrt{\frac{x^4-2x^3}{x^2-4} }\]

that'd make more sense

Then we have
\[(x-1)^2 = \frac{x^3(x-2)}{(x-2)(x+2)}\]

This version is MUCH easier :-)

YUP!!! MUCH MUCH EASIER!!!

I did like the look of the other one in factored form, though :-)

Working on it. Sorry, I suck at math. xD

-4x+x+2=0

Right. And what is -4x + x?

Come on, you're really close to the answer!

-3x+2.

\[-3x+2 = 0\]Add 3x to both sides, and then divide both sides by 3 to get x = ????

x=0.66?

I'd keep it in exact form: x = 2/3

You lost me. D: