9x^4-2x^3+16x^2=0

Solution for 9x^4-2x^3+16x^2=0 equation:

Simplifying
9x4 + -2x3 + 16x2 = 0

Reorder the terms:
16x2 + -2x3 + 9x4 = 0

Solving
16x2 + -2x3 + 9x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(16 + -2x + 9x2) = 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 '(16 + -2x + 9x2)' equal to zero and attempt to solve:

Simplifying
16 + -2x + 9x2 = 0

Solving
16 + -2x + 9x2 = 0

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

Divide each side by '9'.
1.777777778 + -0.2222222222x + x2 = 0

Move the constant term to the right:

Add '-1.777777778' to each side of the equation.
1.777777778 + -0.2222222222x + -1.777777778 + x2 = 0 + -1.777777778

Reorder the terms:
1.777777778 + -1.777777778 + -0.2222222222x + x2 = 0 + -1.777777778

Combine like terms: 1.777777778 + -1.777777778 = 0.000000000
0.000000000 + -0.2222222222x + x2 = 0 + -1.777777778
-0.2222222222x + x2 = 0 + -1.777777778

Combine like terms: 0 + -1.777777778 = -1.777777778
-0.2222222222x + x2 = -1.777777778

The x term is -0.2222222222x.  Take half its coefficient (-0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
-0.2222222222x + 0.01234567901 + x2 = -1.777777778 + 0.01234567901

Reorder the terms:
0.01234567901 + -0.2222222222x + x2 = -1.777777778 + 0.01234567901

Combine like terms: -1.777777778 + 0.01234567901 = -1.76543209899
0.01234567901 + -0.2222222222x + x2 = -1.76543209899

Factor a perfect square on the left side:
(x + -0.1111111111)(x + -0.1111111111) = -1.76543209899

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}