x^4=x^3-5x^2

Solution for x^4=x^3-5x^2 equation:

Simplifying
x4 = x3 + -5x2

Reorder the terms:
x4 = -5x2 + x3

Solving
x4 = -5x2 + x3

Solving for variable 'x'.

Reorder the terms:
5x2 + -1x3 + x4 = -5x2 + x3 + 5x2 + -1x3

Reorder the terms:
5x2 + -1x3 + x4 = -5x2 + 5x2 + x3 + -1x3

Combine like terms: -5x2 + 5x2 = 0
5x2 + -1x3 + x4 = 0 + x3 + -1x3
5x2 + -1x3 + x4 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
5x2 + -1x3 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(5 + -1x + x2) = 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 '(5 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x + x2 = 0

Solving
5 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -1x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -1x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x + x2 = 0 + -5
-1x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x + x2 = -5

The x term is -1x.  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.
-1x + 0.25 + x2 = -5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -5 + 0.25

Combine like terms: -5 + 0.25 = -4.75
0.25 + -1x + x2 = -4.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -4.75

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}