8x^4+2x^3+x^2=0

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Solution for 8x^4+2x^3+x^2=0 equation: 


Simplifying
8x4 + 2x3 + x2 = 0

Reorder the terms:
x2 + 2x3 + 8x4 = 0

Solving
x2 + 2x3 + 8x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(1 + 2x + 8x2) = 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 '(1 + 2x + 8x2)' equal to zero and attempt to solve:

Simplifying
1 + 2x + 8x2 = 0

Solving
1 + 2x + 8x2 = 0

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

Divide each side by '8'.
0.125 + 0.25x + x2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + 0.25x + -0.125 + x2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + 0.25x + x2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + 0.25x + x2 = 0 + -0.125
0.25x + x2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
0.25x + x2 = -0.125

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = -0.125 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = -0.125 + 0.015625

Combine like terms: -0.125 + 0.015625 = -0.109375
0.015625 + 0.25x + x2 = -0.109375

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = -0.109375

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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