Question

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

Answer 1

x^2 - 1 = 0
x^2 -1^2 = 0
(x + 1) (x - 1) = 0
x + 1 = 0 or x - 1 = 0
x = -1 or x = 1

Ans: -1 and 1

Answer 2

(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