I have done 3√(4x-2)+1=√(36x+1) I know its 11/4 but how do I show my work?

Question

anonymous · Answer

how did u get the answer in the first place?

anonymous · Answer

calculator

anonymous · Answer

Square both sides to get rid of the square root on the right:
$$(3\sqrt{4x-2}+1)(3\sqrt{4x-2}+1) = 36x+1$$ =  (\sqrt{36x+1})^{2}\]
That leaves you with:

anonymous · Answer

best thing to do is get rid of the radicals... keep them separated with the equal sign..

anonymous · Answer

Can you multiply what is on the left hand side?

campbell_st · Answer

but you will basically end up with a radical in the expansion...

anonymous · Answer

that's one way.... ^^^^

anonymous · Answer

how does it end up asa fraction? isn't that what x is?

campbell_st · Answer

if you expand the perfect square 

and collect like terms 

you'll end up with a radical expression on the left and a rational number on the right... 

some simple manipulation will give 11/4 as the solution

campbell_st · Answer

$$(3\sqrt{(4x -2)} + 1)^2 = 36x + 1$$

anonymous · Answer

On the left you should get: $$9(4x-2)+ 6\sqrt{4x-2}+1 = 36x+1$$
Move everything to the right that is not a radical, then get rid of the radical like I did at the begining

campbell_st · Answer

you'll need to square both sides after collecting like terms.. 

but you will only be squaring a rational number

then solve for x

anonymous · Answer

ok then distrubute

anonymous · Answer

Move 9(4x-2) to the right side by subtracting it from both sides.
Also move the 1 to the right hand side by subtracting 1 from both sides. What do you get when you do this?

anonymous · Answer

You should have:
$$6\sqrt{4x-2} = 36x+1-9(4x-2) -1$$
Simplify what's on the right. The square both sides:
$$(6\sqrt{4x-2})^2 = (18)^{2}$$
You should end up with:
$$36(4x-2) = 324$$
Then solve for x from here

anonymous · Answer

@KG777  did you get 11/4 as the answer?

anonymous · Answer

http://www.wolframalpha.com/input/?i=3%E2%88%9A%284x-2%29%2B1%3D%E2%88%9A%2836x%2B1%29

anonymous · Answer

@KG777  did you understand all the steps I took to get to the last expression I posted?

anonymous · Answer

yes

anonymous · Answer

Good deal then apply it to any other questions like this and you should be able to solve for x. Good luck!