x^4=4x^2-3

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

Simplifying
x4 = 4x2 + -3

Reorder the terms:
x4 = -3 + 4x2

Solving
x4 = -3 + 4x2

Solving for variable 'x'.

Reorder the terms:
3 + -4x2 + x4 = -3 + 4x2 + 3 + -4x2

Reorder the terms:
3 + -4x2 + x4 = -3 + 3 + 4x2 + -4x2

Combine like terms: -3 + 3 = 0
3 + -4x2 + x4 = 0 + 4x2 + -4x2
3 + -4x2 + x4 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
3 + -4x2 + x4 = 0

Factor a trinomial.
(1 + -1x2)(3 + -1x2) = 0

Factor a difference between two squares.
((1 + x)(1 + -1x))(3 + -1x2) = 0

Subproblem 1
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
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 = {-1.732050808, 1.732050808, -1, 1}