x^4+x^3+20x^2=0

Solution for x^4+x^3+20x^2=0 equation:

Simplifying
x4 + x3 + 20x2 = 0

Reorder the terms:
20x2 + x3 + x4 = 0

Solving
20x2 + x3 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(20 + x + 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 '(20 + x + x2)' equal to zero and attempt to solve:

Simplifying
20 + x + x2 = 0

Solving
20 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + x + x2 = 0 + -20
x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
x + x2 = -20

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.
x + 0.25 + x2 = -20 + 0.25

Reorder the terms:
0.25 + x + x2 = -20 + 0.25

Combine like terms: -20 + 0.25 = -19.75
0.25 + x + x2 = -19.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -19.75

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}