x^4+2x^2-30=0

Solution for x^4+2x^2-30=0 equation:

Simplifying
x4 + 2x2 + -30 = 0

Reorder the terms:
-30 + 2x2 + x4 = 0

Solving
-30 + 2x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 2x2 + 30 + x4 = 0 + 30

Reorder the terms:
-30 + 30 + 2x2 + x4 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 2x2 + x4 = 0 + 30
2x2 + x4 = 0 + 30

Combine like terms: 0 + 30 = 30
2x2 + x4 = 30

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 = 30 + 1

Reorder the terms:
1 + 2x2 + x4 = 30 + 1

Combine like terms: 30 + 1 = 31
1 + 2x2 + x4 = 31

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x2 + 1) equal to 5.567764363 and -5.567764363.

Subproblem 1
x2 + 1 = 5.567764363

Simplifying
x2 + 1 = 5.567764363

Reorder the terms:
1 + x2 = 5.567764363

Solving
1 + x2 = 5.567764363

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 = 5.567764363 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = 5.567764363 + -1
x2 = 5.567764363 + -1

Combine like terms: 5.567764363 + -1 = 4.567764363
x2 = 4.567764363

Simplifying
x2 = 4.567764363

Take the square root of each side:
x = {-2.137232875, 2.137232875}

Subproblem 2
x2 + 1 = -5.567764363

Simplifying
x2 + 1 = -5.567764363

Reorder the terms:
1 + x2 = -5.567764363

Solving
1 + x2 = -5.567764363

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 = -5.567764363 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = -5.567764363 + -1
x2 = -5.567764363 + -1

Combine like terms: -5.567764363 + -1 = -6.567764363
x2 = -6.567764363

Simplifying
x2 = -6.567764363

Reorder the terms:
6.567764363 + x2 = -6.567764363 + 6.567764363

Combine like terms: -6.567764363 + 6.567764363 = 0.000000000
6.567764363 + 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.