can someone please solve -(1/6)+(x/2)(16+x^2)^(-1/2)=0 for x?

Question

anonymous · Answer

Ok, I got it this time, sorry for wrong solution posted initially.  This equation can be rewritten as $$\frac{ 1 }{ 6} = \frac{ x }{ 2\sqrt{16 + x^2} }$$
Then Multiply both sides by denominators to eliminate fractions.  This results in $$2\sqrt{16 + x^2} = 6x$$
Divide both sides by two to isolate the radical, then square both sides to eliminate the radical.  This results in $$16 + x^2 = 9x^2 $$
Then subtract both sides by x^2 and then solve for x (I will leave these rudimentary steps for you to work on!).  The final answer should be $$x =\pm \sqrt{2}$$