4.375x^4-3.75x^2+0.375=0

Solution for 4.375x^4-3.75x^2+0.375=0 equation:

Simplifying
4.375x4 + -3.75x2 + 0.375 = 0

Reorder the terms:
0.375 + -3.75x2 + 4.375x4 = 0

Solving
0.375 + -3.75x2 + 4.375x4 = 0

Solving for variable 'x'.

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

Divide each side by '4.375'.
0.08571428571 + -0.8571428571x2 + x4 = 0

Move the constant term to the right:

Add '-0.08571428571' to each side of the equation.
0.08571428571 + -0.8571428571x2 + -0.08571428571 + x4 = 0 + -0.08571428571

Reorder the terms:
0.08571428571 + -0.08571428571 + -0.8571428571x2 + x4 = 0 + -0.08571428571

Combine like terms: 0.08571428571 + -0.08571428571 = 0.00000000000
0.00000000000 + -0.8571428571x2 + x4 = 0 + -0.08571428571
-0.8571428571x2 + x4 = 0 + -0.08571428571

Combine like terms: 0 + -0.08571428571 = -0.08571428571
-0.8571428571x2 + x4 = -0.08571428571

The x term is -0.8571428571x2.  Take half its coefficient (-0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
-0.8571428571x2 + 0.1836734694 + x4 = -0.08571428571 + 0.1836734694

Reorder the terms:
0.1836734694 + -0.8571428571x2 + x4 = -0.08571428571 + 0.1836734694

Combine like terms: -0.08571428571 + 0.1836734694 = 0.09795918369
0.1836734694 + -0.8571428571x2 + x4 = 0.09795918369

Factor a perfect square on the left side:
(x2 + -0.4285714286)(x2 + -0.4285714286) = 0.09795918369

Calculate the square root of the right side: 0.312984319

Break this problem into two subproblems by setting 
(x2 + -0.4285714286) equal to 0.312984319 and -0.312984319.

Subproblem 1
x2 + -0.4285714286 = 0.312984319

Simplifying
x2 + -0.4285714286 = 0.312984319

Reorder the terms:
-0.4285714286 + x2 = 0.312984319

Solving
-0.4285714286 + x2 = 0.312984319

Solving for variable 'x'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + x2 = 0.312984319 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + x2 = 0.312984319 + 0.4285714286
x2 = 0.312984319 + 0.4285714286

Combine like terms: 0.312984319 + 0.4285714286 = 0.7415557476
x2 = 0.7415557476

Simplifying
x2 = 0.7415557476

Take the square root of each side:
x = {-0.861136312, 0.861136312}

Subproblem 2
x2 + -0.4285714286 = -0.312984319

Simplifying
x2 + -0.4285714286 = -0.312984319

Reorder the terms:
-0.4285714286 + x2 = -0.312984319

Solving
-0.4285714286 + x2 = -0.312984319

Solving for variable 'x'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + x2 = -0.312984319 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + x2 = -0.312984319 + 0.4285714286
x2 = -0.312984319 + 0.4285714286

Combine like terms: -0.312984319 + 0.4285714286 = 0.1155871096
x2 = 0.1155871096

Simplifying
x2 = 0.1155871096

Take the square root of each side:
x = {-0.339981043, 0.339981043}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.861136312, 0.861136312, -0.339981043, 0.339981043}