0=x^4-11x^3+31x^2

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Solution for 0=x^4-11x^3+31x^2 equation: 


Simplifying
0 = x4 + -11x3 + 31x2

Reorder the terms:
0 = 31x2 + -11x3 + x4

Solving
0 = 31x2 + -11x3 + x4

Solving for variable 'x'.
Remove the zero:
-31x2 + 11x3 + -1x4 = 31x2 + -11x3 + x4 + -31x2 + 11x3 + -1x4

Reorder the terms:
-31x2 + 11x3 + -1x4 = 31x2 + -31x2 + -11x3 + 11x3 + x4 + -1x4

Combine like terms: 31x2 + -31x2 = 0
-31x2 + 11x3 + -1x4 = 0 + -11x3 + 11x3 + x4 + -1x4
-31x2 + 11x3 + -1x4 = -11x3 + 11x3 + x4 + -1x4

Combine like terms: -11x3 + 11x3 = 0
-31x2 + 11x3 + -1x4 = 0 + x4 + -1x4
-31x2 + 11x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-31x2 + 11x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-31 + 11x + -1x2) = 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 '(-31 + 11x + -1x2)' equal to zero and attempt to solve:

Simplifying
-31 + 11x + -1x2 = 0

Solving
-31 + 11x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
31 + -11x + x2 = 0

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + -11x + -31 + x2 = 0 + -31

Reorder the terms:
31 + -31 + -11x + x2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -11x + x2 = 0 + -31
-11x + x2 = 0 + -31

Combine like terms: 0 + -31 = -31
-11x + x2 = -31

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -31 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -31 + 30.25

Combine like terms: -31 + 30.25 = -0.75
30.25 + -11x + x2 = -0.75

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = -0.75

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}

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