a^6+7a^3+6=2

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Solution for a^6+7a^3+6=2 equation: 


Simplifying
a6 + 7a3 + 6 = 2

Reorder the terms:
6 + 7a3 + a6 = 2

Solving
6 + 7a3 + a6 = 2

Solving for variable 'a'.

Reorder the terms:
6 + -2 + 7a3 + a6 = 2 + -2

Combine like terms: 6 + -2 = 4
4 + 7a3 + a6 = 2 + -2

Combine like terms: 2 + -2 = 0
4 + 7a3 + a6 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 7a3 + -4 + a6 = 0 + -4

Reorder the terms:
4 + -4 + 7a3 + a6 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7a3 + a6 = 0 + -4
7a3 + a6 = 0 + -4

Combine like terms: 0 + -4 = -4
7a3 + a6 = -4

The a term is 7a3.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7a3 + 12.25 + a6 = -4 + 12.25

Reorder the terms:
12.25 + 7a3 + a6 = -4 + 12.25

Combine like terms: -4 + 12.25 = 8.25
12.25 + 7a3 + a6 = 8.25

Factor a perfect square on the left side:
(a3 + 3.5)(a3 + 3.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(a3 + 3.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
a3 + 3.5 = 2.872281323

Simplifying
a3 + 3.5 = 2.872281323

Reorder the terms:
3.5 + a3 = 2.872281323

Solving
3.5 + a3 = 2.872281323

Solving for variable 'a'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + a3 = 2.872281323 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a3 = 2.872281323 + -3.5
a3 = 2.872281323 + -3.5

Combine like terms: 2.872281323 + -3.5 = -0.627718677
a3 = -0.627718677

Simplifying
a3 = -0.627718677

Reorder the terms:
0.627718677 + a3 = -0.627718677 + 0.627718677

Combine like terms: -0.627718677 + 0.627718677 = 0.000000000
0.627718677 + a3 = 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
a3 + 3.5 = -2.872281323

Simplifying
a3 + 3.5 = -2.872281323

Reorder the terms:
3.5 + a3 = -2.872281323

Solving
3.5 + a3 = -2.872281323

Solving for variable 'a'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + a3 = -2.872281323 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a3 = -2.872281323 + -3.5
a3 = -2.872281323 + -3.5

Combine like terms: -2.872281323 + -3.5 = -6.372281323
a3 = -6.372281323

Simplifying
a3 = -6.372281323

Reorder the terms:
6.372281323 + a3 = -6.372281323 + 6.372281323

Combine like terms: -6.372281323 + 6.372281323 = 0.000000000
6.372281323 + a3 = 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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