Simplifying
x^{2} + -1 = 0
Reorder the terms:
-1 + x^{2} = 0
Solving
-1 + x^{2} = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '1' to each side of the equation.
-1 + 1 + x^{2} = 0 + 1
Combine like terms: -1 + 1 = 0
0 + x^{2} = 0 + 1
x^{2} = 0 + 1
Combine like terms: 0 + 1 = 1
x^{2} = 1
Simplifying
x^{2} = 1
Reorder the terms:
-1 + x^{2} = 1 + -1
Combine like terms: 1 + -1 = 0
-1 + x^{2} = 0
Factor a difference between two squares.
(1 + x)(-1 + x) = 0
#### Subproblem 1

Set the factor '(1 + x)' equal to zero and attempt to solve:
Simplifying
1 + x = 0
Solving
1 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1
Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1
Combine like terms: 0 + -1 = -1
x = -1
Simplifying
x = -1
#### Subproblem 2

Set the factor '(-1 + x)' equal to zero and attempt to solve:
Simplifying
-1 + x = 0
Solving
-1 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '1' to each side of the equation.
-1 + 1 + x = 0 + 1
Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1
Combine like terms: 0 + 1 = 1
x = 1
Simplifying
x = 1#### Solution

x = {-1, 1}