0=0.25x^4-x^3+x^2

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Solution for 0=0.25x^4-x^3+x^2 equation: 


Simplifying
0 = 0.25x4 + -1x3 + x2

Reorder the terms:
0 = x2 + -1x3 + 0.25x4

Solving
0 = x2 + -1x3 + 0.25x4

Solving for variable 'x'.
Remove the zero:
-1x2 + x3 + -0.25x4 = x2 + -1x3 + 0.25x4 + -1x2 + x3 + -0.25x4

Reorder the terms:
-1x2 + x3 + -0.25x4 = x2 + -1x2 + -1x3 + x3 + 0.25x4 + -0.25x4

Combine like terms: x2 + -1x2 = 0
-1x2 + x3 + -0.25x4 = 0 + -1x3 + x3 + 0.25x4 + -0.25x4
-1x2 + x3 + -0.25x4 = -1x3 + x3 + 0.25x4 + -0.25x4

Combine like terms: -1x3 + x3 = 0
-1x2 + x3 + -0.25x4 = 0 + 0.25x4 + -0.25x4
-1x2 + x3 + -0.25x4 = 0.25x4 + -0.25x4

Combine like terms: 0.25x4 + -0.25x4 = 0.00
-1x2 + x3 + -0.25x4 = 0.00

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-1 + x + -0.25x2) = 0.00


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 + x + -0.25x2)' equal to zero and attempt to solve:

Simplifying
-1 + x + -0.25x2 = 0

Solving
-1 + x + -0.25x2 = 0

Begin completing the square.  Divide all terms by
-0.25 the coefficient of the squared term: 

Divide each side by '-0.25'.
4 + -4x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -4x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -4x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -4x + x2 = 0 + -4
-4x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-4x + x2 = -4

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

Add '0.25' to each side of the equation.
-4x + 0.25 + x2 = -4 + 0.25

Reorder the terms:
0.25 + -4x + x2 = -4 + 0.25

Combine like terms: -4 + 0.25 = -3.75
0.25 + -4x + x2 = -3.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -3.75

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}

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