2a^4-6a^3+22a^2=0

Solution for 2a^4-6a^3+22a^2=0 equation:

Simplifying
2a4 + -6a3 + 22a2 = 0

Reorder the terms:
22a2 + -6a3 + 2a4 = 0

Solving
22a2 + -6a3 + 2a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a2'.
2a2(11 + -3a + a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(11 + -3a + a2)' equal to zero and attempt to solve:

Simplifying
11 + -3a + a2 = 0

Solving
11 + -3a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -3a + -11 + a2 = 0 + -11

Reorder the terms:
11 + -11 + -3a + a2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3a + a2 = 0 + -11
-3a + a2 = 0 + -11

Combine like terms: 0 + -11 = -11
-3a + a2 = -11

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = -11 + 2.25

Reorder the terms:
2.25 + -3a + a2 = -11 + 2.25

Combine like terms: -11 + 2.25 = -8.75
2.25 + -3a + a2 = -8.75

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = -8.75

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
a = {0}