4x^4-12x^2=5

Solution for 4x^4-12x^2=5 equation:

Simplifying
4x4 + -12x2 = 5

Reorder the terms:
-12x2 + 4x4 = 5

Solving
-12x2 + 4x4 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + -12x2 + 4x4 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -12x2 + 4x4 = 0

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

Divide each side by '4'.
-1.25 + -3x2 + x4 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -3x2 + 1.25 + x4 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -3x2 + x4 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -3x2 + x4 = 0 + 1.25
-3x2 + x4 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-3x2 + x4 = 1.25

The x term is -3x2.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x2 + 2.25 + x4 = 1.25 + 2.25

Reorder the terms:
2.25 + -3x2 + x4 = 1.25 + 2.25

Combine like terms: 1.25 + 2.25 = 3.5
2.25 + -3x2 + x4 = 3.5

Factor a perfect square on the left side:
(x2 + -1.5)(x2 + -1.5) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(x2 + -1.5) equal to 1.870828693 and -1.870828693.

Subproblem 1
x2 + -1.5 = 1.870828693

Simplifying
x2 + -1.5 = 1.870828693

Reorder the terms:
-1.5 + x2 = 1.870828693

Solving
-1.5 + x2 = 1.870828693

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x2 = 1.870828693 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x2 = 1.870828693 + 1.5
x2 = 1.870828693 + 1.5

Combine like terms: 1.870828693 + 1.5 = 3.370828693
x2 = 3.370828693

Simplifying
x2 = 3.370828693

Take the square root of each side:
x = {-1.83598167, 1.83598167}

Subproblem 2
x2 + -1.5 = -1.870828693

Simplifying
x2 + -1.5 = -1.870828693

Reorder the terms:
-1.5 + x2 = -1.870828693

Solving
-1.5 + x2 = -1.870828693

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x2 = -1.870828693 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x2 = -1.870828693 + 1.5
x2 = -1.870828693 + 1.5

Combine like terms: -1.870828693 + 1.5 = -0.370828693
x2 = -0.370828693

Simplifying
x2 = -0.370828693

Reorder the terms:
0.370828693 + x2 = -0.370828693 + 0.370828693

Combine like terms: -0.370828693 + 0.370828693 = 0.000000000
0.370828693 + 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.