What is the solution of the equation x^2-1=0

(x^2 - 1) factors. This is a basic factoring procedure. Make sure you know it
Solve it like this 
x^2 - a^2 = (x + a)(x - a)

so for x^2 - 1 you get
(x + sqrt(1) )  (x - sqrt(1) = (x + 1)(x-1) 
x^2 - 1 = (x + 1)(x - 1)

(x - 1)(x + 1) =0
x - 1 =0
x = 1

x + 1 = 0
x = - 1

The two answers are x = 1 and x = - 1
You might want to try these. If you post the answers, I'll tell you how you did. Just make comments
x^2 - 25 = 0
x^2 - 9 =0
x^2 - 36 = 0
x^2 - 49 = 0