0=x^4-12x^2-14

Solution for 0=x^4-12x^2-14 equation:

Simplifying
0 = x4 + -12x2 + -14

Reorder the terms:
0 = -14 + -12x2 + x4

Solving
0 = -14 + -12x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 14 = 14
14 + 12x2 + -1x4 = -14 + -12x2 + x4 + 14 + 12x2 + -1x4

Reorder the terms:
14 + 12x2 + -1x4 = -14 + 14 + -12x2 + 12x2 + x4 + -1x4

Combine like terms: -14 + 14 = 0
14 + 12x2 + -1x4 = 0 + -12x2 + 12x2 + x4 + -1x4
14 + 12x2 + -1x4 = -12x2 + 12x2 + x4 + -1x4

Combine like terms: -12x2 + 12x2 = 0
14 + 12x2 + -1x4 = 0 + x4 + -1x4
14 + 12x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
14 + 12x2 + -1x4 = 0

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

Divide each side by '-1'.
-14 + -12x2 + x4 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -12x2 + 14 + x4 = 0 + 14

Reorder the terms:
-14 + 14 + -12x2 + x4 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -12x2 + x4 = 0 + 14
-12x2 + x4 = 0 + 14

Combine like terms: 0 + 14 = 14
-12x2 + x4 = 14

The x term is -12x2.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x2 + 36 + x4 = 14 + 36

Reorder the terms:
36 + -12x2 + x4 = 14 + 36

Combine like terms: 14 + 36 = 50
36 + -12x2 + x4 = 50

Factor a perfect square on the left side:
(x2 + -6)(x2 + -6) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(x2 + -6) equal to 7.071067812 and -7.071067812.

Subproblem 1
x2 + -6 = 7.071067812

Simplifying
x2 + -6 = 7.071067812

Reorder the terms:
-6 + x2 = 7.071067812

Solving
-6 + x2 = 7.071067812

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x2 = 7.071067812 + 6

Combine like terms: -6 + 6 = 0
0 + x2 = 7.071067812 + 6
x2 = 7.071067812 + 6

Combine like terms: 7.071067812 + 6 = 13.071067812
x2 = 13.071067812

Simplifying
x2 = 13.071067812

Take the square root of each side:
x = {-3.615393175, 3.615393175}

Subproblem 2
x2 + -6 = -7.071067812

Simplifying
x2 + -6 = -7.071067812

Reorder the terms:
-6 + x2 = -7.071067812

Solving
-6 + x2 = -7.071067812

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x2 = -7.071067812 + 6

Combine like terms: -6 + 6 = 0
0 + x2 = -7.071067812 + 6
x2 = -7.071067812 + 6

Combine like terms: -7.071067812 + 6 = -1.071067812
x2 = -1.071067812

Simplifying
x2 = -1.071067812

Reorder the terms:
1.071067812 + x2 = -1.071067812 + 1.071067812

Combine like terms: -1.071067812 + 1.071067812 = 0.000000000
1.071067812 + 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.