Solve Radical Equations like a Pro with This Proven TRICK!

[@ashokdubey8415]

Domain:(-9,0)U(5,infinity)
After squarring & simplification the given equation transformed to
x^4+15x^3-1125x-5625=0
=> x=+/-5sqrt(3)

[@Quest3669]

Let (x+10)= t solving gives t+(25/t)= 20 ;5 only 20 valid for real solns. Gives
x= +-5√3 both valid real solns.

[@jackliu1982]

(x+10)^2/25^2=(x+9)/x/(x-5)
(x+10)^2/25^2=14/[5(x-5)]-9/(5x)
(x+10)^2=14*5*25/(x-5)-9*5*25/x
(x+10)^2=1750/(x-5)-1125/x
x(x-5)(x^2+20x+100)=625x+5625
x^4+15x^3-1125x-5625=0
x^4-75^2+15x(x^2-75)=0
(x^2-75)(x^2+75)+15(x^2-75)=0
(x^2-75)(x^2+15x+75)=0
x={5√3, -5√3}

[@davidseed2939]

another way
(x+10)²/25 = ((x+10)/5)²
25(x-9)/x(x-5)
(x/5+2)²=
(x-9)/(x/5)/(x/5-1)
b=x/5
(b+2)² =(5b-9)/(b²-b)
(b²+4b+4)(b²-b) =5b-9
b⁴-3b³+4b²-4b²-4b =5b-9
b⁴-3b³ -9b+9=0
oops