9x^3=5x^2+x

Solution for 9x^3=5x^2+x equation:

Simplifying
9x3 = 5x2 + x

Reorder the terms:
9x3 = x + 5x2

Solving
9x3 = x + 5x2

Solving for variable 'x'.

Reorder the terms:
-1x + -5x2 + 9x3 = x + 5x2 + -1x + -5x2

Reorder the terms:
-1x + -5x2 + 9x3 = x + -1x + 5x2 + -5x2

Combine like terms: x + -1x = 0
-1x + -5x2 + 9x3 = 0 + 5x2 + -5x2
-1x + -5x2 + 9x3 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-1x + -5x2 + 9x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + -5x + 9x2) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + -5x + 9x2)' equal to zero and attempt to solve:

Simplifying
-1 + -5x + 9x2 = 0

Solving
-1 + -5x + 9x2 = 0

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

Divide each side by '9'.
-0.1111111111 + -0.5555555556x + x2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + -0.5555555556x + 0.1111111111 + x2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + -0.5555555556x + x2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + -0.5555555556x + x2 = 0 + 0.1111111111
-0.5555555556x + x2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
-0.5555555556x + x2 = 0.1111111111

The x term is -0.5555555556x.  Take half its coefficient (-0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
-0.5555555556x + 0.07716049384 + x2 = 0.1111111111 + 0.07716049384

Reorder the terms:
0.07716049384 + -0.5555555556x + x2 = 0.1111111111 + 0.07716049384

Combine like terms: 0.1111111111 + 0.07716049384 = 0.18827160494
0.07716049384 + -0.5555555556x + x2 = 0.18827160494

Factor a perfect square on the left side:
(x + -0.2777777778)(x + -0.2777777778) = 0.18827160494

Calculate the square root of the right side: 0.43390276

Break this problem into two subproblems by setting 
(x + -0.2777777778) equal to 0.43390276 and -0.43390276.

Subproblem 1
x + -0.2777777778 = 0.43390276

Simplifying
x + -0.2777777778 = 0.43390276

Reorder the terms:
-0.2777777778 + x = 0.43390276

Solving
-0.2777777778 + x = 0.43390276

Solving for variable 'x'.

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

Add '0.2777777778' to each side of the equation.
-0.2777777778 + 0.2777777778 + x = 0.43390276 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + x = 0.43390276 + 0.2777777778
x = 0.43390276 + 0.2777777778

Combine like terms: 0.43390276 + 0.2777777778 = 0.7116805378
x = 0.7116805378

Simplifying
x = 0.7116805378

Subproblem 2
x + -0.2777777778 = -0.43390276

Simplifying
x + -0.2777777778 = -0.43390276

Reorder the terms:
-0.2777777778 + x = -0.43390276

Solving
-0.2777777778 + x = -0.43390276

Solving for variable 'x'.

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

Add '0.2777777778' to each side of the equation.
-0.2777777778 + 0.2777777778 + x = -0.43390276 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + x = -0.43390276 + 0.2777777778
x = -0.43390276 + 0.2777777778

Combine like terms: -0.43390276 + 0.2777777778 = -0.1561249822
x = -0.1561249822

Simplifying
x = -0.1561249822

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7116805378, -0.1561249822}
Solution
x = {0, 0.7116805378, -0.1561249822}