Question 1040517
Solve for x:
sqrt(x)/4+x/1100 = 14
(275*sqrt(x)+x)/1100 = 14
275*sqrt(x)+x = 15400
275*sqrt(x) = 15400-x
75625x = (15400-x)^2
75625x = x^2-30800x+237160000
-x^2+106425x-237160000 = 0
x^2-106425 x+237160000 = 0
x^2-106425 x = -237160000
x^2-106425 x+11326280625/4 = 10377640625/4
(x-106425/2)^2 = 10377640625/4
x-106425/2 = (1375*sqrt(5489))/2 or x-106425/2 = -(1375*sqrt(5489))/2
x = 106425/2+(1375*sqrt(5489))/2 or x-106425/2 = -(1375*sqrt(5489))/2
x = 106425/2+(1375*sqrt(5489))/2 or x = 106425/2-(1375*sqrt(5489))/2
sqrt(x)/4+x/1100 => 1/4 sqrt(106425/2-(1375*sqrt(5489))/2)+(106425/2-(1375 sqrt(5489))/2)/1100  =  1/4*sqrt(106425/2-(1375*sqrt(5489))/2)+(106425/2-(1375*sqrt(5489))/2)/1100 ~~ 14
So this solution is correct. You can do the other one and you will see it's incorrect. Therefore, the solution is:
x = 106425/2-(1375*sqrt(5489))/2 You don't need me to finish it off, use  your calculator.