Solving an equation with radicals

[trulyfalse]

Hello and good evening! I'm having a fair bit of difficulty with this question, any help would be appreciated.

Homework Statement

√(x²/2+11)=x-1
Answers are required in mixed radical form.

Homework Equations

The quadratic formula/factoring will be useful near the end of the problem.

The Attempt at a Solution

I squared both sides of the equation to get
x²/2+11=x²+1
However I'm not quite sure how to proceed and whether eliminating the radical in the first step was the correct step.

 

[Dick]

You are doing the right step but you squared the right side wrong. (x-1)^2 isn't equal to x^2+1. Try that again.

 

[trulyfalse]

You're right! I completely forgot it was a binomial. Thanks for your help.