x^4-2x^3+18x^2=0

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Solution for x^4-2x^3+18x^2=0 equation: 


Simplifying
x4 + -2x3 + 18x2 = 0

Reorder the terms:
18x2 + -2x3 + x4 = 0

Solving
18x2 + -2x3 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(18 + -2x + x2) = 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 '(18 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
18 + -2x + x2 = 0

Solving
18 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -2x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -2x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -2x + x2 = 0 + -18
-2x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-2x + x2 = -18

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 = -18 + 1

Reorder the terms:
1 + -2x + x2 = -18 + 1

Combine like terms: -18 + 1 = -17
1 + -2x + x2 = -17

Factor a perfect square on the left side:
(x + -1)(x + -1) = -17

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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