4x^12-5x^6-14=0

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Solution for 4x^12-5x^6-14=0 equation: 


Simplifying
4x12 + -5x6 + -14 = 0

Reorder the terms:
-14 + -5x6 + 4x12 = 0

Solving
-14 + -5x6 + 4x12 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-3.5 + -1.25x6 + x12 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -1.25x6 + 3.5 + x12 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -1.25x6 + x12 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -1.25x6 + x12 = 0 + 3.5
-1.25x6 + x12 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-1.25x6 + x12 = 3.5

The x term is -1.25x6.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x6 + 0.390625 + x12 = 3.5 + 0.390625

Reorder the terms:
0.390625 + -1.25x6 + x12 = 3.5 + 0.390625

Combine like terms: 3.5 + 0.390625 = 3.890625
0.390625 + -1.25x6 + x12 = 3.890625

Factor a perfect square on the left side:
(x6 + -0.625)(x6 + -0.625) = 3.890625

Calculate the square root of the right side: 1.97246673

Break this problem into two subproblems by setting 
(x6 + -0.625) equal to 1.97246673 and -1.97246673.


Subproblem 1
x6 + -0.625 = 1.97246673

Simplifying
x6 + -0.625 = 1.97246673

Reorder the terms:
-0.625 + x6 = 1.97246673

Solving
-0.625 + x6 = 1.97246673

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x6 = 1.97246673 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x6 = 1.97246673 + 0.625
x6 = 1.97246673 + 0.625

Combine like terms: 1.97246673 + 0.625 = 2.59746673
x6 = 2.59746673

Simplifying
x6 = 2.59746673

Reorder the terms:
-2.59746673 + x6 = 2.59746673 + -2.59746673

Combine like terms: 2.59746673 + -2.59746673 = 0.00000000
-2.59746673 + x6 = 0.00000000

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


Subproblem 2
x6 + -0.625 = -1.97246673

Simplifying
x6 + -0.625 = -1.97246673

Reorder the terms:
-0.625 + x6 = -1.97246673

Solving
-0.625 + x6 = -1.97246673

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x6 = -1.97246673 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x6 = -1.97246673 + 0.625
x6 = -1.97246673 + 0.625

Combine like terms: -1.97246673 + 0.625 = -1.34746673
x6 = -1.34746673

Simplifying
x6 = -1.34746673

Reorder the terms:
1.34746673 + x6 = -1.34746673 + 1.34746673

Combine like terms: -1.34746673 + 1.34746673 = 0.00000000
1.34746673 + x6 = 0.00000000

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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