x^2+x^3+x^4+5x^2=0

Solution for x^2+x^3+x^4+5x^2=0 equation:

Simplifying
x2 + x3 + x4 + 5x2 = 0

Reorder the terms:
x2 + 5x2 + x3 + x4 = 0

Combine like terms: x2 + 5x2 = 6x2
6x2 + x3 + x4 = 0

Solving
6x2 + x3 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(6 + 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 '(6 + x + x2)' equal to zero and attempt to solve:

Simplifying
6 + x + x2 = 0

Solving
6 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x + x2 = 0 + -6
x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
x + x2 = -6

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 = -6 + 0.25

Reorder the terms:
0.25 + x + x2 = -6 + 0.25

Combine like terms: -6 + 0.25 = -5.75
0.25 + x + x2 = -5.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -5.75

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}