x^4-4x^2-49=0

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Solution for x^4-4x^2-49=0 equation: 


Simplifying
x4 + -4x2 + -49 = 0

Reorder the terms:
-49 + -4x2 + x4 = 0

Solving
-49 + -4x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -4x2 + 49 + x4 = 0 + 49

Reorder the terms:
-49 + 49 + -4x2 + x4 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -4x2 + x4 = 0 + 49
-4x2 + x4 = 0 + 49

Combine like terms: 0 + 49 = 49
-4x2 + x4 = 49

The x term is -4x2.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x2 + 4 + x4 = 49 + 4

Reorder the terms:
4 + -4x2 + x4 = 49 + 4

Combine like terms: 49 + 4 = 53
4 + -4x2 + x4 = 53

Factor a perfect square on the left side:
(x2 + -2)(x2 + -2) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(x2 + -2) equal to 7.280109889 and -7.280109889.


Subproblem 1
x2 + -2 = 7.280109889

Simplifying
x2 + -2 = 7.280109889

Reorder the terms:
-2 + x2 = 7.280109889

Solving
-2 + x2 = 7.280109889

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x2 = 7.280109889 + 2

Combine like terms: -2 + 2 = 0
0 + x2 = 7.280109889 + 2
x2 = 7.280109889 + 2

Combine like terms: 7.280109889 + 2 = 9.280109889
x2 = 9.280109889

Simplifying
x2 = 9.280109889

Take the square root of each side:
x = {-3.046327279, 3.046327279}


Subproblem 2
x2 + -2 = -7.280109889

Simplifying
x2 + -2 = -7.280109889

Reorder the terms:
-2 + x2 = -7.280109889

Solving
-2 + x2 = -7.280109889

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x2 = -7.280109889 + 2

Combine like terms: -2 + 2 = 0
0 + x2 = -7.280109889 + 2
x2 = -7.280109889 + 2

Combine like terms: -7.280109889 + 2 = -5.280109889
x2 = -5.280109889

Simplifying
x2 = -5.280109889

Reorder the terms:
5.280109889 + x2 = -5.280109889 + 5.280109889

Combine like terms: -5.280109889 + 5.280109889 = 0.000000000
5.280109889 + 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.

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