16x^12+8x^6-1=0

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Solution for 16x^12+8x^6-1=0 equation: 


Simplifying
16x12 + 8x6 + -1 = 0

Reorder the terms:
-1 + 8x6 + 16x12 = 0

Solving
-1 + 8x6 + 16x12 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
-0.0625 + 0.5x6 + x12 = 0

Move the constant term to the right:

Add '0.0625' to each side of the equation.
-0.0625 + 0.5x6 + 0.0625 + x12 = 0 + 0.0625

Reorder the terms:
-0.0625 + 0.0625 + 0.5x6 + x12 = 0 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + 0.5x6 + x12 = 0 + 0.0625
0.5x6 + x12 = 0 + 0.0625

Combine like terms: 0 + 0.0625 = 0.0625
0.5x6 + x12 = 0.0625

The x term is 0.5x6.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x6 + 0.0625 + x12 = 0.0625 + 0.0625

Reorder the terms:
0.0625 + 0.5x6 + x12 = 0.0625 + 0.0625

Combine like terms: 0.0625 + 0.0625 = 0.125
0.0625 + 0.5x6 + x12 = 0.125

Factor a perfect square on the left side:
(x6 + 0.25)(x6 + 0.25) = 0.125

Calculate the square root of the right side: 0.353553391

Break this problem into two subproblems by setting 
(x6 + 0.25) equal to 0.353553391 and -0.353553391.


Subproblem 1
x6 + 0.25 = 0.353553391

Simplifying
x6 + 0.25 = 0.353553391

Reorder the terms:
0.25 + x6 = 0.353553391

Solving
0.25 + x6 = 0.353553391

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x6 = 0.353553391 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x6 = 0.353553391 + -0.25
x6 = 0.353553391 + -0.25

Combine like terms: 0.353553391 + -0.25 = 0.103553391
x6 = 0.103553391

Simplifying
x6 = 0.103553391

Reorder the terms:
-0.103553391 + x6 = 0.103553391 + -0.103553391

Combine like terms: 0.103553391 + -0.103553391 = 0.000000000
-0.103553391 + x6 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.


Subproblem 2
x6 + 0.25 = -0.353553391

Simplifying
x6 + 0.25 = -0.353553391

Reorder the terms:
0.25 + x6 = -0.353553391

Solving
0.25 + x6 = -0.353553391

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x6 = -0.353553391 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x6 = -0.353553391 + -0.25
x6 = -0.353553391 + -0.25

Combine like terms: -0.353553391 + -0.25 = -0.603553391
x6 = -0.603553391

Simplifying
x6 = -0.603553391

Reorder the terms:
0.603553391 + x6 = -0.603553391 + 0.603553391

Combine like terms: -0.603553391 + 0.603553391 = 0.000000000
0.603553391 + x6 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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