10X^4-6X^3+8X^2=0

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Solution for 10X^4-6X^3+8X^2=0 equation: 


Simplifying
10X4 + -6X3 + 8X2 = 0

Reorder the terms:
8X2 + -6X3 + 10X4 = 0

Solving
8X2 + -6X3 + 10X4 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2X2'.
2X2(4 + -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 '(4 + -3X + 5X2)' equal to zero and attempt to solve:

Simplifying
4 + -3X + 5X2 = 0

Solving
4 + -3X + 5X2 = 0

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

Divide each side by '5'.
0.8 + -0.6X + X2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -0.6X + -0.8 + X2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -0.6X + X2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -0.6X + X2 = 0 + -0.8
-0.6X + X2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-0.6X + X2 = -0.8

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 = -0.8 + 0.09

Reorder the terms:
0.09 + -0.6X + X2 = -0.8 + 0.09

Combine like terms: -0.8 + 0.09 = -0.71
0.09 + -0.6X + X2 = -0.71

Factor a perfect square on the left side:
(X + -0.3)(X + -0.3) = -0.71

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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