How can I simplify this complex expression?

[white1995gt]

I need the following expression simplified.

36/[64.4*(0.5+(2+ x)*((1-(1/4)*x^2 )^0.5)) ]-x*((1-(1/4)*x^2 )^0.5)=0

 

[Mark44]

What have you tried?

Also, this is an equation, so the likely thing to do would be to solve it for x.

 

[white1995gt]

I just need to simplify first then I have to solve for x. I got the following once I factored everything out and simplified things:

(259*x^8)+(1037*x^7)-(1037*x^6)-(8294*x^5)-(4406*x^4)+(16589*x^3)+(17626*x^2)

 

[white1995gt]

Actually I think I'm wrong. I think I could get it if someone could square the following expression for me:

64.64 * [0.5 + (2 + x) * (Sqrt[1 - (0.25*x^2)])]

I just can't get it no matter what I try.

 

[Mark44]

I need the following expression simplified.

36/[64.4*(0.5+(2+ x)*((1-(1/4)*x^2 )^0.5)) ]-x*((1-(1/4)*x^2 )^0.5)=0

Is this the equation?
$$\frac{36}{64.4(1/2 + (2 + x)\sqrt{1 - x^2/4})} - \frac{x}{\sqrt{1 - x^2/4}} = 0$$

If so, you can write it as
$$\frac{36}{64.4(1/2 + (2 + x)\sqrt{1 - x^2/4})} = \frac{x}{\sqrt{1 - x^2/4}}$$

You can square both sides. I would move the 64.4 up into the numerator so that the new first numerator is 36/64.4 and the denominator of the expression on the left is
$$(1/2 + (2 + x)\sqrt{1 - x^2/4})$$

The square of this expression is (1/2)^2 + 2(1/2)(2 + x)sqrt(1 + x^2/4) + (2 + x)^2 * (1 - x^2/4). Everything else is pretty straightforward.

 

[white1995gt]

It's actually this:

$$\frac{36}{64.4(1/2 + (2 + x)\sqrt{1 - x^2/4}} ) - {x}{\sqrt{1 - x^2/4}} = 0$$

 

[Mark44]

Rewrite as $$\frac{36/64.4}{1/2 + (2 + x)\sqrt{1 - x^2/4}} = {x}{\sqrt{1 - x^2/4}}$$

and multiply both sides by sqrt(1 - x^2/4).

 

[white1995gt]

I'm not really sure how to simplify the radical because it's inside the parenthesis. I doubt it's as simple as this:

$$<br /> \frac{36/64.4} {1/2 + (2 + x)} = {x}(1 - x^2/4)$$

Sorry that the parenthesis aren't closed I'm still trying to get used to posting here.

 

[Mark44]

Rewrite as $$\frac{36/64.4}{1/2 + (2 + x)\sqrt{1 - x^2/4}} = {x}{\sqrt{1 - x^2/4}}$$

and multiply both sides by sqrt(1 - x^2/4).

On second thought, I think it makes more sense to multiply both sides by what's in the denominator on the left side.

 

[white1995gt]

Thank you for all the help. I got mathematica the other day and just got the answer after playing around with it a little bit.