Question 574632
Tricky!


Let's not solve for X right away, but X^2.  Does that help?
X^4-81=0
(x^2 - )(X^2 + ) = 0  (We need to find two factors of 81.)
9x9 = 81  Aha!
(X^2 - 9)(X^2 + 9) = 0  Now factor as you would normally, but using X^2 as terms


Left paren first:
X^2 - 9 = 0  
X^2 = 9
Sqrt(X^2) = Sqrt(9)
X = 3 or -3


Right paren:
X^2 + 9 = 0
X^2 = -9
Depending on your grade, either this is impossible - or an irrational possibility. ;-) I'm going to guess you're not into irrational numbers yet.  But if you are, you can still take it from here.  By the way, this is how we get more than the two solutions we did above.


Checking:
X^4 - 81 = 0
(3)^4 - 81 = 0
81 - 81 = 0  Correct!


AND
X^4 - 81 = 0
(-3)^4 - 81 = 0
81 - 81 = 0  Correct!