10x^4-8x^3+2x^2=0

Solution for 10x^4-8x^3+2x^2=0 equation:

Simplifying
10x4 + -8x3 + 2x2 = 0

Reorder the terms:
2x2 + -8x3 + 10x4 = 0

Solving
2x2 + -8x3 + 10x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(1 + -4x + 5x2) = 0

Ignore the factor 2.
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 '(1 + -4x + 5x2)' equal to zero and attempt to solve:

Simplifying
1 + -4x + 5x2 = 0

Solving
1 + -4x + 5x2 = 0

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

Divide each side by '5'.
0.2 + -0.8x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -0.8x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -0.8x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -0.8x + x2 = 0 + -0.2
-0.8x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-0.8x + x2 = -0.2

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = -0.2 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = -0.2 + 0.16

Combine like terms: -0.2 + 0.16 = -0.04
0.16 + -0.8x + x2 = -0.04

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = -0.04

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}