x^4=3x^2-2

Solution for x^4=3x^2-2 equation:

Simplifying
x4 = 3x2 + -2

Reorder the terms:
x4 = -2 + 3x2

Solving
x4 = -2 + 3x2

Solving for variable 'x'.

Reorder the terms:
2 + -3x2 + x4 = -2 + 3x2 + 2 + -3x2

Reorder the terms:
2 + -3x2 + x4 = -2 + 2 + 3x2 + -3x2

Combine like terms: -2 + 2 = 0
2 + -3x2 + x4 = 0 + 3x2 + -3x2
2 + -3x2 + x4 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
2 + -3x2 + x4 = 0

Factor a trinomial.
(1 + -1x2)(2 + -1x2) = 0

Factor a difference between two squares.
((1 + x)(1 + -1x))(2 + -1x2) = 0

Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
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
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-1.414213562, 1.414213562, -1, 1}