4x^4+49x^2+25=0

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Solution for 4x^4+49x^2+25=0 equation: 


Simplifying
4x4 + 49x2 + 25 = 0

Reorder the terms:
25 + 49x2 + 4x4 = 0

Solving
25 + 49x2 + 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'.
6.25 + 12.25x2 + x4 = 0

Move the constant term to the right:

Add '-6.25' to each side of the equation.
6.25 + 12.25x2 + -6.25 + x4 = 0 + -6.25

Reorder the terms:
6.25 + -6.25 + 12.25x2 + x4 = 0 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + 12.25x2 + x4 = 0 + -6.25
12.25x2 + x4 = 0 + -6.25

Combine like terms: 0 + -6.25 = -6.25
12.25x2 + x4 = -6.25

The x term is 12.25x2.  Take half its coefficient (6.125).
Square it (37.515625) and add it to both sides.

Add '37.515625' to each side of the equation.
12.25x2 + 37.515625 + x4 = -6.25 + 37.515625

Reorder the terms:
37.515625 + 12.25x2 + x4 = -6.25 + 37.515625

Combine like terms: -6.25 + 37.515625 = 31.265625
37.515625 + 12.25x2 + x4 = 31.265625

Factor a perfect square on the left side:
(x2 + 6.125)(x2 + 6.125) = 31.265625

Calculate the square root of the right side: 5.591567312

Break this problem into two subproblems by setting 
(x2 + 6.125) equal to 5.591567312 and -5.591567312.


Subproblem 1
x2 + 6.125 = 5.591567312

Simplifying
x2 + 6.125 = 5.591567312

Reorder the terms:
6.125 + x2 = 5.591567312

Solving
6.125 + x2 = 5.591567312

Solving for variable 'x'.

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

Add '-6.125' to each side of the equation.
6.125 + -6.125 + x2 = 5.591567312 + -6.125

Combine like terms: 6.125 + -6.125 = 0.000
0.000 + x2 = 5.591567312 + -6.125
x2 = 5.591567312 + -6.125

Combine like terms: 5.591567312 + -6.125 = -0.533432688
x2 = -0.533432688

Simplifying
x2 = -0.533432688

Reorder the terms:
0.533432688 + x2 = -0.533432688 + 0.533432688

Combine like terms: -0.533432688 + 0.533432688 = 0.000000000
0.533432688 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.


Subproblem 2
x2 + 6.125 = -5.591567312

Simplifying
x2 + 6.125 = -5.591567312

Reorder the terms:
6.125 + x2 = -5.591567312

Solving
6.125 + x2 = -5.591567312

Solving for variable 'x'.

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

Add '-6.125' to each side of the equation.
6.125 + -6.125 + x2 = -5.591567312 + -6.125

Combine like terms: 6.125 + -6.125 = 0.000
0.000 + x2 = -5.591567312 + -6.125
x2 = -5.591567312 + -6.125

Combine like terms: -5.591567312 + -6.125 = -11.716567312
x2 = -11.716567312

Simplifying
x2 = -11.716567312

Reorder the terms:
11.716567312 + x2 = -11.716567312 + 11.716567312

Combine like terms: -11.716567312 + 11.716567312 = 0.000000000
11.716567312 + 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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