2x^4-48x^2-25=0

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Solution for 2x^4-48x^2-25=0 equation: 


Simplifying
2x4 + -48x2 + -25 = 0

Reorder the terms:
-25 + -48x2 + 2x4 = 0

Solving
-25 + -48x2 + 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 + -24x2 + x4 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -24x2 + 12.5 + x4 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -24x2 + x4 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -24x2 + x4 = 0 + 12.5
-24x2 + x4 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
-24x2 + x4 = 12.5

The x term is -24x2.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x2 + 144 + x4 = 12.5 + 144

Reorder the terms:
144 + -24x2 + x4 = 12.5 + 144

Combine like terms: 12.5 + 144 = 156.5
144 + -24x2 + x4 = 156.5

Factor a perfect square on the left side:
(x2 + -12)(x2 + -12) = 156.5

Calculate the square root of the right side: 12.509996003

Break this problem into two subproblems by setting 
(x2 + -12) equal to 12.509996003 and -12.509996003.


Subproblem 1
x2 + -12 = 12.509996003

Simplifying
x2 + -12 = 12.509996003

Reorder the terms:
-12 + x2 = 12.509996003

Solving
-12 + x2 = 12.509996003

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x2 = 12.509996003 + 12

Combine like terms: -12 + 12 = 0
0 + x2 = 12.509996003 + 12
x2 = 12.509996003 + 12

Combine like terms: 12.509996003 + 12 = 24.509996003
x2 = 24.509996003

Simplifying
x2 = 24.509996003

Take the square root of each side:
x = {-4.950757114, 4.950757114}


Subproblem 2
x2 + -12 = -12.509996003

Simplifying
x2 + -12 = -12.509996003

Reorder the terms:
-12 + x2 = -12.509996003

Solving
-12 + x2 = -12.509996003

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x2 = -12.509996003 + 12

Combine like terms: -12 + 12 = 0
0 + x2 = -12.509996003 + 12
x2 = -12.509996003 + 12

Combine like terms: -12.509996003 + 12 = -0.509996003
x2 = -0.509996003

Simplifying
x2 = -0.509996003

Reorder the terms:
0.509996003 + x2 = -0.509996003 + 0.509996003

Combine like terms: -0.509996003 + 0.509996003 = 0.000000000
0.509996003 + 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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