Question

Can you find x for this equation? Also, please show your work... I can't figure out how you got your answer otherwise!
12+sqrt(4*(9/7)(x-24)) = 3+sqrt(4*2.25(x-6))
You can see the equation better here...
http://i.imgur.com/AQjFl.gif

Answer 1

\[12+\sqrt{4\times(9/7)(x-24)} = 3+\sqrt{4\times2.25(x-6)}\]
\[\implies12+\sqrt{(36/7)(x-24)} = 3+\sqrt{9(x-6)}\]
\[\implies9 = \sqrt{9(x-6)}-\sqrt{(36/7)(x-24)}\]
squaring both sides
\[\implies81 =9(x-6) +(36/7)(x−24)-2\sqrt{9(x-6)}\sqrt{(36/7)(x-24)}\]
\[\implies81 -9(x-6) -(36/7)(x−24)=-2\sqrt{9(x-6)}\sqrt{(36/7)(x-24)}\]
Again square both sides
\[\implies[81 -9(x-6) -(36/7)(x−24)]^2=(-2)^2[{9(x-6)}{(36/7)(x-24)}\]
Now the radical signs have been removed. So now you can proceed in the general way..

Answer 2

Hope you can do the rest

Answer 3

I think so... You've gotten me past the part I've had trouble on... thanks a lot!