1+x^4-2x^2+1.96x^2=1.0096x^4

Solution for 1+x^4-2x^2+1.96x^2=1.0096x^4 equation:

Simplifying
1 + x4 + -2x2 + 1.96x2 = 1.0096x4

Reorder the terms:
1 + -2x2 + 1.96x2 + x4 = 1.0096x4

Combine like terms: -2x2 + 1.96x2 = -0.04x2
1 + -0.04x2 + x4 = 1.0096x4

Solving
1 + -0.04x2 + x4 = 1.0096x4

Solving for variable 'x'.

Combine like terms: x4 + -1.0096x4 = -0.0096x4
1 + -0.04x2 + -0.0096x4 = 1.0096x4 + -1.0096x4

Combine like terms: 1.0096x4 + -1.0096x4 = 0.0000
1 + -0.04x2 + -0.0096x4 = 0.0000

Begin completing the square.  Divide all terms by
-0.0096 the coefficient of the squared term: 

Divide each side by '-0.0096'.
-104.1666667 + 4.166666667x2 + x4 = 0

Move the constant term to the right:

Add '104.1666667' to each side of the equation.
-104.1666667 + 4.166666667x2 + 104.1666667 + x4 = 0 + 104.1666667

Reorder the terms:
-104.1666667 + 104.1666667 + 4.166666667x2 + x4 = 0 + 104.1666667

Combine like terms: -104.1666667 + 104.1666667 = 0.0000000
0.0000000 + 4.166666667x2 + x4 = 0 + 104.1666667
4.166666667x2 + x4 = 0 + 104.1666667

Combine like terms: 0 + 104.1666667 = 104.1666667
4.166666667x2 + x4 = 104.1666667

The x term is 4.166666667x2.  Take half its coefficient (2.083333334).
Square it (4.340277781) and add it to both sides.

Add '4.340277781' to each side of the equation.
4.166666667x2 + 4.340277781 + x4 = 104.1666667 + 4.340277781

Reorder the terms:
4.340277781 + 4.166666667x2 + x4 = 104.1666667 + 4.340277781

Combine like terms: 104.1666667 + 4.340277781 = 108.506944481
4.340277781 + 4.166666667x2 + x4 = 108.506944481

Factor a perfect square on the left side:
(x2 + 2.083333334)(x2 + 2.083333334) = 108.506944481

Calculate the square root of the right side: 10.416666668

Break this problem into two subproblems by setting 
(x2 + 2.083333334) equal to 10.416666668 and -10.416666668.

Subproblem 1
x2 + 2.083333334 = 10.416666668

Simplifying
x2 + 2.083333334 = 10.416666668

Reorder the terms:
2.083333334 + x2 = 10.416666668

Solving
2.083333334 + x2 = 10.416666668

Solving for variable 'x'.

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

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + x2 = 10.416666668 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + x2 = 10.416666668 + -2.083333334
x2 = 10.416666668 + -2.083333334

Combine like terms: 10.416666668 + -2.083333334 = 8.333333334
x2 = 8.333333334

Simplifying
x2 = 8.333333334

Take the square root of each side:
x = {-2.886751346, 2.886751346}

Subproblem 2
x2 + 2.083333334 = -10.416666668

Simplifying
x2 + 2.083333334 = -10.416666668

Reorder the terms:
2.083333334 + x2 = -10.416666668

Solving
2.083333334 + x2 = -10.416666668

Solving for variable 'x'.

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

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + x2 = -10.416666668 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + x2 = -10.416666668 + -2.083333334
x2 = -10.416666668 + -2.083333334

Combine like terms: -10.416666668 + -2.083333334 = -12.500000002
x2 = -12.500000002

Simplifying
x2 = -12.500000002

Reorder the terms:
12.500000002 + x2 = -12.500000002 + 12.500000002

Combine like terms: -12.500000002 + 12.500000002 = 0.000000000
12.500000002 + 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.