2x^4+x^2=4

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Solution for 2x^4+x^2=4 equation: 


Simplifying
2x4 + x2 = 4

Reorder the terms:
x2 + 2x4 = 4

Solving
x2 + 2x4 = 4

Solving for variable 'x'.

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

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

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

Divide each side by '2'.
-2 + 0.5x2 + x4 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 0.5x2 + 2 + x4 = 0 + 2

Reorder the terms:
-2 + 2 + 0.5x2 + x4 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 0.5x2 + x4 = 0 + 2
0.5x2 + x4 = 0 + 2

Combine like terms: 0 + 2 = 2
0.5x2 + x4 = 2

The x term is x2.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5x2 + 0.25 + x4 = 2 + 0.25

Reorder the terms:
0.25 + 0.5x2 + x4 = 2 + 0.25

Combine like terms: 2 + 0.25 = 2.25
0.25 + 0.5x2 + x4 = 2.25

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = 2.25

Calculate the square root of the right side: 1.5

Break this problem into two subproblems by setting 
(x2 + 0.5) equal to 1.5 and -1.5.


Subproblem 1
x2 + 0.5 = 1.5

Simplifying
x2 + 0.5 = 1.5

Reorder the terms:
0.5 + x2 = 1.5

Solving
0.5 + x2 = 1.5

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x2 = 1.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = 1.5 + -0.5
x2 = 1.5 + -0.5

Combine like terms: 1.5 + -0.5 = 1
x2 = 1

Simplifying
x2 = 1

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


Subproblem 2
x2 + 0.5 = -1.5

Simplifying
x2 + 0.5 = -1.5

Reorder the terms:
0.5 + x2 = -1.5

Solving
0.5 + x2 = -1.5

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x2 = -1.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = -1.5 + -0.5
x2 = -1.5 + -0.5

Combine like terms: -1.5 + -0.5 = -2
x2 = -2

Simplifying
x2 = -2

Reorder the terms:
2 + x2 = -2 + 2

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

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.

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