Question 1113670
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<pre>
14 = {{{sqrt(x)/4}}} + {{{x/1100}}}


Let y = {{{sqrt(x)}}} be new variable.  Then the equation takes the form


14 =  {{{y/4}}} + {{{y^2/1100}}}.


Multiply both sides by 1100 to get 


{{{y^2 + 275y - 15400}}} = 0


{{{y[1,2]}}} = {{{(-275 +- sqrt(275^2 + 4*15400))/2}}} = {{{(-250 +- 370.4)/2}}}.


Only positive root works  y = {{{(-250 + 370.4)/2}}} = 47.7.


Then  x = {{{47.7^2}}} =  2275.3 ft.


<U>Check</U>.  {{{sqrt(2275.3)/4}}} + {{{2275.3/1100}}} = 14.


<U>Answer</U>.  The depth of the well is equal to  2275.3 ft.
</pre>

Solved.