a^4+6a^2+3=9

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Solution for a^4+6a^2+3=9 equation:


Simplifying
a4 + 6a2 + 3 = 9

Reorder the terms:
3 + 6a2 + a4 = 9

Solving
3 + 6a2 + a4 = 9

Solving for variable 'a'.

Reorder the terms:
3 + -9 + 6a2 + a4 = 9 + -9

Combine like terms: 3 + -9 = -6
-6 + 6a2 + a4 = 9 + -9

Combine like terms: 9 + -9 = 0
-6 + 6a2 + a4 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 6a2 + 6 + a4 = 0 + 6

Reorder the terms:
-6 + 6 + 6a2 + a4 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 6a2 + a4 = 0 + 6
6a2 + a4 = 0 + 6

Combine like terms: 0 + 6 = 6
6a2 + a4 = 6

The a term is 6a2.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6a2 + 9 + a4 = 6 + 9

Reorder the terms:
9 + 6a2 + a4 = 6 + 9

Combine like terms: 6 + 9 = 15
9 + 6a2 + a4 = 15

Factor a perfect square on the left side:
(a2 + 3)(a2 + 3) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(a2 + 3) equal to 3.872983346 and -3.872983346.

Subproblem 1

a2 + 3 = 3.872983346 Simplifying a2 + 3 = 3.872983346 Reorder the terms: 3 + a2 = 3.872983346 Solving 3 + a2 = 3.872983346 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a2 = 3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + a2 = 3.872983346 + -3 a2 = 3.872983346 + -3 Combine like terms: 3.872983346 + -3 = 0.872983346 a2 = 0.872983346 Simplifying a2 = 0.872983346 Take the square root of each side: a = {-0.934335778, 0.934335778}

Subproblem 2

a2 + 3 = -3.872983346 Simplifying a2 + 3 = -3.872983346 Reorder the terms: 3 + a2 = -3.872983346 Solving 3 + a2 = -3.872983346 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a2 = -3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + a2 = -3.872983346 + -3 a2 = -3.872983346 + -3 Combine like terms: -3.872983346 + -3 = -6.872983346 a2 = -6.872983346 Simplifying a2 = -6.872983346 Reorder the terms: 6.872983346 + a2 = -6.872983346 + 6.872983346 Combine like terms: -6.872983346 + 6.872983346 = 0.000000000 6.872983346 + a2 = 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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