0.125x^4+2.5x^2+3=0

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Solution for 0.125x^4+2.5x^2+3=0 equation: 


Simplifying
0.125x4 + 2.5x2 + 3 = 0

Reorder the terms:
3 + 2.5x2 + 0.125x4 = 0

Solving
3 + 2.5x2 + 0.125x4 = 0

Solving for variable 'x'.

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

Divide each side by '0.125'.
24 + 20x2 + x4 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + 20x2 + -24 + x4 = 0 + -24

Reorder the terms:
24 + -24 + 20x2 + x4 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + 20x2 + x4 = 0 + -24
20x2 + x4 = 0 + -24

Combine like terms: 0 + -24 = -24
20x2 + x4 = -24

The x term is 20x2.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x2 + 100 + x4 = -24 + 100

Reorder the terms:
100 + 20x2 + x4 = -24 + 100

Combine like terms: -24 + 100 = 76
100 + 20x2 + x4 = 76

Factor a perfect square on the left side:
(x2 + 10)(x2 + 10) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(x2 + 10) equal to 8.717797887 and -8.717797887.


Subproblem 1
x2 + 10 = 8.717797887

Simplifying
x2 + 10 = 8.717797887

Reorder the terms:
10 + x2 = 8.717797887

Solving
10 + x2 = 8.717797887

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x2 = 8.717797887 + -10

Combine like terms: 10 + -10 = 0
0 + x2 = 8.717797887 + -10
x2 = 8.717797887 + -10

Combine like terms: 8.717797887 + -10 = -1.282202113
x2 = -1.282202113

Simplifying
x2 = -1.282202113

Reorder the terms:
1.282202113 + x2 = -1.282202113 + 1.282202113

Combine like terms: -1.282202113 + 1.282202113 = 0.000000000
1.282202113 + 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 + 10 = -8.717797887

Simplifying
x2 + 10 = -8.717797887

Reorder the terms:
10 + x2 = -8.717797887

Solving
10 + x2 = -8.717797887

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x2 = -8.717797887 + -10

Combine like terms: 10 + -10 = 0
0 + x2 = -8.717797887 + -10
x2 = -8.717797887 + -10

Combine like terms: -8.717797887 + -10 = -18.717797887
x2 = -18.717797887

Simplifying
x2 = -18.717797887

Reorder the terms:
18.717797887 + x2 = -18.717797887 + 18.717797887

Combine like terms: -18.717797887 + 18.717797887 = 0.000000000
18.717797887 + 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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