4x^4-53x^2-49=0

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Solution for 4x^4-53x^2-49=0 equation: 


Simplifying
4x4 + -53x2 + -49 = 0

Reorder the terms:
-49 + -53x2 + 4x4 = 0

Solving
-49 + -53x2 + 4x4 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-12.25 + -13.25x2 + x4 = 0

Move the constant term to the right:

Add '12.25' to each side of the equation.
-12.25 + -13.25x2 + 12.25 + x4 = 0 + 12.25

Reorder the terms:
-12.25 + 12.25 + -13.25x2 + x4 = 0 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + -13.25x2 + x4 = 0 + 12.25
-13.25x2 + x4 = 0 + 12.25

Combine like terms: 0 + 12.25 = 12.25
-13.25x2 + x4 = 12.25

The x term is -13.25x2.  Take half its coefficient (-6.625).
Square it (43.890625) and add it to both sides.

Add '43.890625' to each side of the equation.
-13.25x2 + 43.890625 + x4 = 12.25 + 43.890625

Reorder the terms:
43.890625 + -13.25x2 + x4 = 12.25 + 43.890625

Combine like terms: 12.25 + 43.890625 = 56.140625
43.890625 + -13.25x2 + x4 = 56.140625

Factor a perfect square on the left side:
(x2 + -6.625)(x2 + -6.625) = 56.140625

Calculate the square root of the right side: 7.492704785

Break this problem into two subproblems by setting 
(x2 + -6.625) equal to 7.492704785 and -7.492704785.


Subproblem 1
x2 + -6.625 = 7.492704785

Simplifying
x2 + -6.625 = 7.492704785

Reorder the terms:
-6.625 + x2 = 7.492704785

Solving
-6.625 + x2 = 7.492704785

Solving for variable 'x'.

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

Add '6.625' to each side of the equation.
-6.625 + 6.625 + x2 = 7.492704785 + 6.625

Combine like terms: -6.625 + 6.625 = 0.000
0.000 + x2 = 7.492704785 + 6.625
x2 = 7.492704785 + 6.625

Combine like terms: 7.492704785 + 6.625 = 14.117704785
x2 = 14.117704785

Simplifying
x2 = 14.117704785

Take the square root of each side:
x = {-3.757353428, 3.757353428}


Subproblem 2
x2 + -6.625 = -7.492704785

Simplifying
x2 + -6.625 = -7.492704785

Reorder the terms:
-6.625 + x2 = -7.492704785

Solving
-6.625 + x2 = -7.492704785

Solving for variable 'x'.

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

Add '6.625' to each side of the equation.
-6.625 + 6.625 + x2 = -7.492704785 + 6.625

Combine like terms: -6.625 + 6.625 = 0.000
0.000 + x2 = -7.492704785 + 6.625
x2 = -7.492704785 + 6.625

Combine like terms: -7.492704785 + 6.625 = -0.867704785
x2 = -0.867704785

Simplifying
x2 = -0.867704785

Reorder the terms:
0.867704785 + x2 = -0.867704785 + 0.867704785

Combine like terms: -0.867704785 + 0.867704785 = 0.000000000
0.867704785 + 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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