Question 987319
.
Your equation is


{{{sqrt(8x)}}} + {{{sqrt(2x)}}}- {{{sqrt(x/8)}}} = {{{110}}}. 


Notice that 


{{{sqrt(8x)}}} = {{{sqrt(8)}}}{{{sqrt(x)}}} = {{{2sqrt(2)}}}{{{sqrt(x)}}},


{{{sqrt(2x)}}} = {{{sqrt(2)}}}{{{sqrt(x)}}},     and 


{{{sqrt(x/8)}}} = {{{sqrt(1/8)}}}{{{sqrt(x)}}} = {{{1/(2sqrt(2))}}}{{{sqrt(x)}}} = {{{sqrt(2)/(2*2)}}}{{{sqrt(x)}}} = {{{sqrt(2)/4}}}{{{sqrt(x)}}}. 


Hence,  your equations takes the form


{{{2sqrt(2)}}}{{{sqrt(x)}}} + {{{sqrt(2)}}}{{{sqrt(x)}}} - {{{sqrt(2)/4}}}{{{sqrt(x)}}} = 110,     or 


{{{(2sqrt(2) + sqrt(2) - sqrt(2)/4)}}}{{{sqrt(x)}}} = 110,


Now,  multiply both sides by  4  and then collect the common terms:


{{{(8sqrt(2) + 4sqrt(2) - sqrt(2))}}}{{{sqrt(x)}}} = 440,


{{{11sqrt(2)}}}{{{sqrt(x)}}} = 440.


Hence, 


{{{sqrt(x)}}} = {{{440/(11sqrt(2))}}} = {{{40/sqrt(2)}}} = {{{(40*sqrt(2))/2}}} = {{{20sqrt(2)}}}.


Therefore,  x = 400*2 = 800.


<B>Answer</B>. &nbsp;x = 800.