10x^4+6x^3+18x^2=0

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Solution for 10x^4+6x^3+18x^2=0 equation: 


Simplifying
10x4 + 6x3 + 18x2 = 0

Reorder the terms:
18x2 + 6x3 + 10x4 = 0

Solving
18x2 + 6x3 + 10x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(9 + 3x + 5x2) = 0

Ignore the factor 2.

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 '(9 + 3x + 5x2)' equal to zero and attempt to solve:

Simplifying
9 + 3x + 5x2 = 0

Solving
9 + 3x + 5x2 = 0

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

Divide each side by '5'.
1.8 + 0.6x + x2 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + 0.6x + -1.8 + x2 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + 0.6x + x2 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + 0.6x + x2 = 0 + -1.8
0.6x + x2 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
0.6x + x2 = -1.8

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = -1.8 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = -1.8 + 0.09

Combine like terms: -1.8 + 0.09 = -1.71
0.09 + 0.6x + x2 = -1.71

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = -1.71

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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