0.0007716x^4-0.0556x^2+0.92284=0

Solution for 0.0007716x^4-0.0556x^2+0.92284=0 equation:

Simplifying
0.0007716x4 + -0.0556x2 + 0.92284 = 0

Reorder the terms:
0.92284 + -0.0556x2 + 0.0007716x4 = 0

Solving
0.92284 + -0.0556x2 + 0.0007716x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.0007716 the coefficient of the squared term: 

Divide each side by '0.0007716'.
1196.008294 + -72.05806117x2 + x4 = 0

Move the constant term to the right:

Add '-1196.008294' to each side of the equation.
1196.008294 + -72.05806117x2 + -1196.008294 + x4 = 0 + -1196.008294

Reorder the terms:
1196.008294 + -1196.008294 + -72.05806117x2 + x4 = 0 + -1196.008294

Combine like terms: 1196.008294 + -1196.008294 = 0.000000
0.000000 + -72.05806117x2 + x4 = 0 + -1196.008294
-72.05806117x2 + x4 = 0 + -1196.008294

Combine like terms: 0 + -1196.008294 = -1196.008294
-72.05806117x2 + x4 = -1196.008294

The x term is -72.05806117x2.  Take half its coefficient (-36.02903059).
Square it (1298.091045) and add it to both sides.

Add '1298.091045' to each side of the equation.
-72.05806117x2 + 1298.091045 + x4 = -1196.008294 + 1298.091045

Reorder the terms:
1298.091045 + -72.05806117x2 + x4 = -1196.008294 + 1298.091045

Combine like terms: -1196.008294 + 1298.091045 = 102.082751
1298.091045 + -72.05806117x2 + x4 = 102.082751

Factor a perfect square on the left side:
(x2 + -36.02903059)(x2 + -36.02903059) = 102.082751

Calculate the square root of the right side: 10.103600893

Break this problem into two subproblems by setting 
(x2 + -36.02903059) equal to 10.103600893 and -10.103600893.

Subproblem 1
x2 + -36.02903059 = 10.103600893

Simplifying
x2 + -36.02903059 = 10.103600893

Reorder the terms:
-36.02903059 + x2 = 10.103600893

Solving
-36.02903059 + x2 = 10.103600893

Solving for variable 'x'.

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

Add '36.02903059' to each side of the equation.
-36.02903059 + 36.02903059 + x2 = 10.103600893 + 36.02903059

Combine like terms: -36.02903059 + 36.02903059 = 0.00000000
0.00000000 + x2 = 10.103600893 + 36.02903059
x2 = 10.103600893 + 36.02903059

Combine like terms: 10.103600893 + 36.02903059 = 46.132631483
x2 = 46.132631483

Simplifying
x2 = 46.132631483

Take the square root of each side:
x = {-6.792100668, 6.792100668}

Subproblem 2
x2 + -36.02903059 = -10.103600893

Simplifying
x2 + -36.02903059 = -10.103600893

Reorder the terms:
-36.02903059 + x2 = -10.103600893

Solving
-36.02903059 + x2 = -10.103600893

Solving for variable 'x'.

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

Add '36.02903059' to each side of the equation.
-36.02903059 + 36.02903059 + x2 = -10.103600893 + 36.02903059

Combine like terms: -36.02903059 + 36.02903059 = 0.00000000
0.00000000 + x2 = -10.103600893 + 36.02903059
x2 = -10.103600893 + 36.02903059

Combine like terms: -10.103600893 + 36.02903059 = 25.925429697
x2 = 25.925429697

Simplifying
x2 = 25.925429697

Take the square root of each side:
x = {-5.091702043, 5.091702043}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-6.792100668, 6.792100668, -5.091702043, 5.091702043}