6X^4+10X^2+5=3X^2-1

Solution for 6X^4+10X^2+5=3X^2-1 equation:

Simplifying
6X4 + 10X2 + 5 = 3X2 + -1

Reorder the terms:
5 + 10X2 + 6X4 = 3X2 + -1

Reorder the terms:
5 + 10X2 + 6X4 = -1 + 3X2

Solving
5 + 10X2 + 6X4 = -1 + 3X2

Solving for variable 'X'.

Reorder the terms:
5 + 1 + 10X2 + -3X2 + 6X4 = -1 + 3X2 + 1 + -3X2

Combine like terms: 5 + 1 = 6
6 + 10X2 + -3X2 + 6X4 = -1 + 3X2 + 1 + -3X2

Combine like terms: 10X2 + -3X2 = 7X2
6 + 7X2 + 6X4 = -1 + 3X2 + 1 + -3X2

Reorder the terms:
6 + 7X2 + 6X4 = -1 + 1 + 3X2 + -3X2

Combine like terms: -1 + 1 = 0
6 + 7X2 + 6X4 = 0 + 3X2 + -3X2
6 + 7X2 + 6X4 = 3X2 + -3X2

Combine like terms: 3X2 + -3X2 = 0
6 + 7X2 + 6X4 = 0

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

Divide each side by '6'.
1 + 1.166666667X2 + X4 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 1.166666667X2 + -1 + X4 = 0 + -1

Reorder the terms:
1 + -1 + 1.166666667X2 + X4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 1.166666667X2 + X4 = 0 + -1
1.166666667X2 + X4 = 0 + -1

Combine like terms: 0 + -1 = -1
1.166666667X2 + X4 = -1

The X term is 1.166666667X2.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667X2 + 0.3402777780 + X4 = -1 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667X2 + X4 = -1 + 0.3402777780

Combine like terms: -1 + 0.3402777780 = -0.659722222
0.3402777780 + 1.166666667X2 + X4 = -0.659722222

Factor a perfect square on the left side:
(X2 + 0.5833333335)(X2 + 0.5833333335) = -0.659722222

Can't calculate square root of the right side.

The solution to this equation could not be determined.