Find all the real solutions to the equation: |x^2 -8|=|9-x|-1. Provide exact solutions (not rounded numbers) please and thank you!

To solve we need to find a way to address the absolute values. We can use the definition: 

 

that means there are four possibilities: 

1) 
 

which leads to 
 

2)
 
which yields complex roots 

3)
 
Which yields extraneous roots 

4)
 
which yields 
x=0, x=1 

:)