hard equation

sqrt (x^2 + 1) + (x^2 + 1)  = 90

Let  u  =   sqrt (x^2 + 1)

And u^2  =(x ^2 + 1)

So  we  have

u + u^2  =  90          rearrange  as

u^2  + u  -  90    =   0      factor

(u + 10)  ( u - 9)   =   0

Set each factor to  0  and solve for u  and we have that

u = -10            u  = 9

This  means  that

sqrt (x^2 + 1)   = -10        this  has no real solutions

         or

sqrt (x^2 + 1)  =  9          square both sides

x^2  + 1   = 81      subtract 1 from both sides

x^2  = 80      take both roots

x = ±√80

x = ±4√5