x^4-50x^2=49

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Solution for x^4-50x^2=49 equation: 


Simplifying
x4 + -50x2 = 49

Reorder the terms:
-50x2 + x4 = 49

Solving
-50x2 + x4 = 49

Solving for variable 'x'.

Reorder the terms:
-49 + -50x2 + x4 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + -50x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -50x2 + 49 + x4 = 0 + 49

Reorder the terms:
-49 + 49 + -50x2 + x4 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -50x2 + x4 = 0 + 49
-50x2 + x4 = 0 + 49

Combine like terms: 0 + 49 = 49
-50x2 + x4 = 49

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 = 49 + 625

Reorder the terms:
625 + -50x2 + x4 = 49 + 625

Combine like terms: 49 + 625 = 674
625 + -50x2 + x4 = 674

Factor a perfect square on the left side:
(x2 + -25)(x2 + -25) = 674

Calculate the square root of the right side: 25.961509971

Break this problem into two subproblems by setting 
(x2 + -25) equal to 25.961509971 and -25.961509971.


Subproblem 1
x2 + -25 = 25.961509971

Simplifying
x2 + -25 = 25.961509971

Reorder the terms:
-25 + x2 = 25.961509971

Solving
-25 + x2 = 25.961509971

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 = 25.961509971 + 25

Combine like terms: -25 + 25 = 0
0 + x2 = 25.961509971 + 25
x2 = 25.961509971 + 25

Combine like terms: 25.961509971 + 25 = 50.961509971
x2 = 50.961509971

Simplifying
x2 = 50.961509971

Take the square root of each side:
x = {-7.138733079, 7.138733079}


Subproblem 2
x2 + -25 = -25.961509971

Simplifying
x2 + -25 = -25.961509971

Reorder the terms:
-25 + x2 = -25.961509971

Solving
-25 + x2 = -25.961509971

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 = -25.961509971 + 25

Combine like terms: -25 + 25 = 0
0 + x2 = -25.961509971 + 25
x2 = -25.961509971 + 25

Combine like terms: -25.961509971 + 25 = -0.961509971
x2 = -0.961509971

Simplifying
x2 = -0.961509971

Reorder the terms:
0.961509971 + x2 = -0.961509971 + 0.961509971

Combine like terms: -0.961509971 + 0.961509971 = 0.000000000
0.961509971 + 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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