x^4+50x^2=1

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Solution for x^4+50x^2=1 equation: 


Simplifying
x4 + 50x2 = 1

Reorder the terms:
50x2 + x4 = 1

Solving
50x2 + x4 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 50x2 + x4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 50x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 50x2 + 1 + x4 = 0 + 1

Reorder the terms:
-1 + 1 + 50x2 + x4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 50x2 + x4 = 0 + 1
50x2 + x4 = 0 + 1

Combine like terms: 0 + 1 = 1
50x2 + x4 = 1

The x term is 50x2.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x2 + 625 + x4 = 1 + 625

Reorder the terms:
625 + 50x2 + x4 = 1 + 625

Combine like terms: 1 + 625 = 626
625 + 50x2 + x4 = 626

Factor a perfect square on the left side:
(x2 + 25)(x2 + 25) = 626

Calculate the square root of the right side: 25.019992006

Break this problem into two subproblems by setting 
(x2 + 25) equal to 25.019992006 and -25.019992006.


Subproblem 1
x2 + 25 = 25.019992006

Simplifying
x2 + 25 = 25.019992006

Reorder the terms:
25 + x2 = 25.019992006

Solving
25 + x2 = 25.019992006

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x2 = 25.019992006 + -25

Combine like terms: 25 + -25 = 0
0 + x2 = 25.019992006 + -25
x2 = 25.019992006 + -25

Combine like terms: 25.019992006 + -25 = 0.019992006
x2 = 0.019992006

Simplifying
x2 = 0.019992006

Take the square root of each side:
x = {-0.14139309, 0.14139309}


Subproblem 2
x2 + 25 = -25.019992006

Simplifying
x2 + 25 = -25.019992006

Reorder the terms:
25 + x2 = -25.019992006

Solving
25 + x2 = -25.019992006

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x2 = -25.019992006 + -25

Combine like terms: 25 + -25 = 0
0 + x2 = -25.019992006 + -25
x2 = -25.019992006 + -25

Combine like terms: -25.019992006 + -25 = -50.019992006
x2 = -50.019992006

Simplifying
x2 = -50.019992006

Reorder the terms:
50.019992006 + x2 = -50.019992006 + 50.019992006

Combine like terms: -50.019992006 + 50.019992006 = 0.000000000
50.019992006 + 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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