2x^4-50x^2-25=0

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Solution for 2x^4-50x^2-25=0 equation: 


Simplifying
2x4 + -50x2 + -25 = 0

Reorder the terms:
-25 + -50x2 + 2x4 = 0

Solving
-25 + -50x2 + 2x4 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-12.5 + -25x2 + x4 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -25x2 + 12.5 + x4 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -25x2 + x4 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -25x2 + x4 = 0 + 12.5
-25x2 + x4 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
-25x2 + x4 = 12.5

The x term is -25x2.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x2 + 156.25 + x4 = 12.5 + 156.25

Reorder the terms:
156.25 + -25x2 + x4 = 12.5 + 156.25

Combine like terms: 12.5 + 156.25 = 168.75
156.25 + -25x2 + x4 = 168.75

Factor a perfect square on the left side:
(x2 + -12.5)(x2 + -12.5) = 168.75

Calculate the square root of the right side: 12.990381057

Break this problem into two subproblems by setting 
(x2 + -12.5) equal to 12.990381057 and -12.990381057.


Subproblem 1
x2 + -12.5 = 12.990381057

Simplifying
x2 + -12.5 = 12.990381057

Reorder the terms:
-12.5 + x2 = 12.990381057

Solving
-12.5 + x2 = 12.990381057

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x2 = 12.990381057 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x2 = 12.990381057 + 12.5
x2 = 12.990381057 + 12.5

Combine like terms: 12.990381057 + 12.5 = 25.490381057
x2 = 25.490381057

Simplifying
x2 = 25.490381057

Take the square root of each side:
x = {-5.048799962, 5.048799962}


Subproblem 2
x2 + -12.5 = -12.990381057

Simplifying
x2 + -12.5 = -12.990381057

Reorder the terms:
-12.5 + x2 = -12.990381057

Solving
-12.5 + x2 = -12.990381057

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x2 = -12.990381057 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x2 = -12.990381057 + 12.5
x2 = -12.990381057 + 12.5

Combine like terms: -12.990381057 + 12.5 = -0.490381057
x2 = -0.490381057

Simplifying
x2 = -0.490381057

Reorder the terms:
0.490381057 + x2 = -0.490381057 + 0.490381057

Combine like terms: -0.490381057 + 0.490381057 = 0.000000000
0.490381057 + 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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