3x^4-6x^3+33x^2=

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Solution for 3x^4-6x^3+33x^2= equation: 


Simplifying
3x4 + -6x3 + 33x2 = 0

Reorder the terms:
33x2 + -6x3 + 3x4 = 0

Solving
33x2 + -6x3 + 3x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(11 + -2x + x2) = 0

Ignore the factor 3.

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 '(11 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
11 + -2x + x2 = 0

Solving
11 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -2x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + -2x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x + x2 = 0 + -11
-2x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-2x + x2 = -11

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -11 + 1

Reorder the terms:
1 + -2x + x2 = -11 + 1

Combine like terms: -11 + 1 = -10
1 + -2x + x2 = -10

Factor a perfect square on the left side:
(x + -1)(x + -1) = -10

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}

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