121+198x^6+8x^12=0

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Solution for 121+198x^6+8x^12=0 equation:


Simplifying
121 + 198x6 + 8x12 = 0

Solving
121 + 198x6 + 8x12 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
15.125 + 24.75x6 + x12 = 0

Move the constant term to the right:

Add '-15.125' to each side of the equation.
15.125 + 24.75x6 + -15.125 + x12 = 0 + -15.125

Reorder the terms:
15.125 + -15.125 + 24.75x6 + x12 = 0 + -15.125

Combine like terms: 15.125 + -15.125 = 0.000
0.000 + 24.75x6 + x12 = 0 + -15.125
24.75x6 + x12 = 0 + -15.125

Combine like terms: 0 + -15.125 = -15.125
24.75x6 + x12 = -15.125

The x term is 24.75x6.  Take half its coefficient (12.375).
Square it (153.140625) and add it to both sides.

Add '153.140625' to each side of the equation.
24.75x6 + 153.140625 + x12 = -15.125 + 153.140625

Reorder the terms:
153.140625 + 24.75x6 + x12 = -15.125 + 153.140625

Combine like terms: -15.125 + 153.140625 = 138.015625
153.140625 + 24.75x6 + x12 = 138.015625

Factor a perfect square on the left side:
(x6 + 12.375)(x6 + 12.375) = 138.015625

Calculate the square root of the right side: 11.74800515

Break this problem into two subproblems by setting 
(x6 + 12.375) equal to 11.74800515 and -11.74800515.

Subproblem 1

x6 + 12.375 = 11.74800515 Simplifying x6 + 12.375 = 11.74800515 Reorder the terms: 12.375 + x6 = 11.74800515 Solving 12.375 + x6 = 11.74800515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.375' to each side of the equation. 12.375 + -12.375 + x6 = 11.74800515 + -12.375 Combine like terms: 12.375 + -12.375 = 0.000 0.000 + x6 = 11.74800515 + -12.375 x6 = 11.74800515 + -12.375 Combine like terms: 11.74800515 + -12.375 = -0.62699485 x6 = -0.62699485 Simplifying x6 = -0.62699485 Reorder the terms: 0.62699485 + x6 = -0.62699485 + 0.62699485 Combine like terms: -0.62699485 + 0.62699485 = 0.00000000 0.62699485 + 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 + 12.375 = -11.74800515 Simplifying x6 + 12.375 = -11.74800515 Reorder the terms: 12.375 + x6 = -11.74800515 Solving 12.375 + x6 = -11.74800515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.375' to each side of the equation. 12.375 + -12.375 + x6 = -11.74800515 + -12.375 Combine like terms: 12.375 + -12.375 = 0.000 0.000 + x6 = -11.74800515 + -12.375 x6 = -11.74800515 + -12.375 Combine like terms: -11.74800515 + -12.375 = -24.12300515 x6 = -24.12300515 Simplifying x6 = -24.12300515 Reorder the terms: 24.12300515 + x6 = -24.12300515 + 24.12300515 Combine like terms: -24.12300515 + 24.12300515 = 0.00000000 24.12300515 + 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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