2x^4-x^3=-2x^2

Solution for 2x^4-x^3=-2x^2 equation:

Simplifying
2x4 + -1x3 = -2x2

Reorder the terms:
-1x3 + 2x4 = -2x2

Solving
-1x3 + 2x4 = -2x2

Solving for variable 'x'.

Reorder the terms:
2x2 + -1x3 + 2x4 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
2x2 + -1x3 + 2x4 = 0

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

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 '(2 + -1x + 2x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x + 2x2 = 0

Solving
2 + -1x + 2x2 = 0

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

Divide each side by '2'.
1 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -0.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -0.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -0.5x + x2 = 0 + -1
-0.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-0.5x + x2 = -1

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -1 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -1 + 0.0625

Combine like terms: -1 + 0.0625 = -0.9375
0.0625 + -0.5x + x2 = -0.9375

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -0.9375

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}