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

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


Simplifying
4x4 + x2 + -49 = 0

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

Solving
-49 + x2 + 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 + 0.25x2 + x4 = 0

Move the constant term to the right:

Add '12.25' to each side of the equation.
-12.25 + 0.25x2 + 12.25 + x4 = 0 + 12.25

Reorder the terms:
-12.25 + 12.25 + 0.25x2 + x4 = 0 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + 0.25x2 + x4 = 0 + 12.25
0.25x2 + x4 = 0 + 12.25

Combine like terms: 0 + 12.25 = 12.25
0.25x2 + x4 = 12.25

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.
0.25x2 + 0.25 + x4 = 12.25 + 0.25

Reorder the terms:
0.25 + 0.25x2 + x4 = 12.25 + 0.25

Combine like terms: 12.25 + 0.25 = 12.5
0.25 + 0.25x2 + x4 = 12.5

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = 12.5

Calculate the square root of the right side: 3.535533906

Break this problem into two subproblems by setting 
(x2 + 0.5) equal to 3.535533906 and -3.535533906.


Subproblem 1
x2 + 0.5 = 3.535533906

Simplifying
x2 + 0.5 = 3.535533906

Reorder the terms:
0.5 + x2 = 3.535533906

Solving
0.5 + x2 = 3.535533906

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 = 3.535533906 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = 3.535533906 + -0.5
x2 = 3.535533906 + -0.5

Combine like terms: 3.535533906 + -0.5 = 3.035533906
x2 = 3.035533906

Simplifying
x2 = 3.035533906

Take the square root of each side:
x = {-1.742278366, 1.742278366}


Subproblem 2
x2 + 0.5 = -3.535533906

Simplifying
x2 + 0.5 = -3.535533906

Reorder the terms:
0.5 + x2 = -3.535533906

Solving
0.5 + x2 = -3.535533906

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 = -3.535533906 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = -3.535533906 + -0.5
x2 = -3.535533906 + -0.5

Combine like terms: -3.535533906 + -0.5 = -4.035533906
x2 = -4.035533906

Simplifying
x2 = -4.035533906

Reorder the terms:
4.035533906 + x2 = -4.035533906 + 4.035533906

Combine like terms: -4.035533906 + 4.035533906 = 0.000000000
4.035533906 + 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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