-x^4+1=2x^2-3

Solution for -x^4+1=2x^2-3 equation:

Simplifying
-1x4 + 1 = 2x2 + -3

Reorder the terms:
1 + -1x4 = 2x2 + -3

Reorder the terms:
1 + -1x4 = -3 + 2x2

Solving
1 + -1x4 = -3 + 2x2

Solving for variable 'x'.

Reorder the terms:
1 + 3 + -2x2 + -1x4 = -3 + 2x2 + 3 + -2x2

Combine like terms: 1 + 3 = 4
4 + -2x2 + -1x4 = -3 + 2x2 + 3 + -2x2

Reorder the terms:
4 + -2x2 + -1x4 = -3 + 3 + 2x2 + -2x2

Combine like terms: -3 + 3 = 0
4 + -2x2 + -1x4 = 0 + 2x2 + -2x2
4 + -2x2 + -1x4 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
4 + -2x2 + -1x4 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + 2x2 + x4 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 2x2 + 4 + x4 = 0 + 4

Reorder the terms:
-4 + 4 + 2x2 + x4 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 2x2 + x4 = 0 + 4
2x2 + x4 = 0 + 4

Combine like terms: 0 + 4 = 4
2x2 + x4 = 4

The x term is 2x2.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x2 + 1 + x4 = 4 + 1

Reorder the terms:
1 + 2x2 + x4 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + 2x2 + x4 = 5

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x2 + 1) equal to 2.236067978 and -2.236067978.

Subproblem 1
x2 + 1 = 2.236067978

Simplifying
x2 + 1 = 2.236067978

Reorder the terms:
1 + x2 = 2.236067978

Solving
1 + x2 = 2.236067978

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 + x2 = 2.236067978 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = 2.236067978 + -1
x2 = 2.236067978 + -1

Combine like terms: 2.236067978 + -1 = 1.236067978
x2 = 1.236067978

Simplifying
x2 = 1.236067978

Take the square root of each side:
x = {-1.111785941, 1.111785941}

Subproblem 2
x2 + 1 = -2.236067978

Simplifying
x2 + 1 = -2.236067978

Reorder the terms:
1 + x2 = -2.236067978

Solving
1 + x2 = -2.236067978

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 + x2 = -2.236067978 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = -2.236067978 + -1
x2 = -2.236067978 + -1

Combine like terms: -2.236067978 + -1 = -3.236067978
x2 = -3.236067978

Simplifying
x2 = -3.236067978

Reorder the terms:
3.236067978 + x2 = -3.236067978 + 3.236067978

Combine like terms: -3.236067978 + 3.236067978 = 0.000000000
3.236067978 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.