12x^6-5x^4+25x^2=0

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Solution for 12x^6-5x^4+25x^2=0 equation: 


Simplifying
12x6 + -5x4 + 25x2 = 0

Reorder the terms:
25x2 + -5x4 + 12x6 = 0

Solving
25x2 + -5x4 + 12x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(25 + -5x2 + 12x4) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(25 + -5x2 + 12x4)' equal to zero and attempt to solve:

Simplifying
25 + -5x2 + 12x4 = 0

Solving
25 + -5x2 + 12x4 = 0

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

Divide each side by '12'.
2.083333333 + -0.4166666667x2 + x4 = 0

Move the constant term to the right:

Add '-2.083333333' to each side of the equation.
2.083333333 + -0.4166666667x2 + -2.083333333 + x4 = 0 + -2.083333333

Reorder the terms:
2.083333333 + -2.083333333 + -0.4166666667x2 + x4 = 0 + -2.083333333

Combine like terms: 2.083333333 + -2.083333333 = 0.000000000
0.000000000 + -0.4166666667x2 + x4 = 0 + -2.083333333
-0.4166666667x2 + x4 = 0 + -2.083333333

Combine like terms: 0 + -2.083333333 = -2.083333333
-0.4166666667x2 + x4 = -2.083333333

The x term is -0.4166666667x2.  Take half its coefficient (-0.2083333334).
Square it (0.04340277781) and add it to both sides.

Add '0.04340277781' to each side of the equation.
-0.4166666667x2 + 0.04340277781 + x4 = -2.083333333 + 0.04340277781

Reorder the terms:
0.04340277781 + -0.4166666667x2 + x4 = -2.083333333 + 0.04340277781

Combine like terms: -2.083333333 + 0.04340277781 = -2.03993055519
0.04340277781 + -0.4166666667x2 + x4 = -2.03993055519

Factor a perfect square on the left side:
(x2 + -0.2083333334)(x2 + -0.2083333334) = -2.03993055519

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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