2a^4-6a^2-9=0

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Solution for 2a^4-6a^2-9=0 equation:


Simplifying
2a4 + -6a2 + -9 = 0

Reorder the terms:
-9 + -6a2 + 2a4 = 0

Solving
-9 + -6a2 + 2a4 = 0

Solving for variable 'a'.

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

Divide each side by '2'.
-4.5 + -3a2 + a4 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -3a2 + 4.5 + a4 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -3a2 + a4 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -3a2 + a4 = 0 + 4.5
-3a2 + a4 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-3a2 + a4 = 4.5

The a term is -3a2.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a2 + 2.25 + a4 = 4.5 + 2.25

Reorder the terms:
2.25 + -3a2 + a4 = 4.5 + 2.25

Combine like terms: 4.5 + 2.25 = 6.75
2.25 + -3a2 + a4 = 6.75

Factor a perfect square on the left side:
(a2 + -1.5)(a2 + -1.5) = 6.75

Calculate the square root of the right side: 2.598076211

Break this problem into two subproblems by setting 
(a2 + -1.5) equal to 2.598076211 and -2.598076211.

Subproblem 1

a2 + -1.5 = 2.598076211 Simplifying a2 + -1.5 = 2.598076211 Reorder the terms: -1.5 + a2 = 2.598076211 Solving -1.5 + a2 = 2.598076211 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a2 = 2.598076211 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a2 = 2.598076211 + 1.5 a2 = 2.598076211 + 1.5 Combine like terms: 2.598076211 + 1.5 = 4.098076211 a2 = 4.098076211 Simplifying a2 = 4.098076211 Take the square root of each side: a = {-2.024370572, 2.024370572}

Subproblem 2

a2 + -1.5 = -2.598076211 Simplifying a2 + -1.5 = -2.598076211 Reorder the terms: -1.5 + a2 = -2.598076211 Solving -1.5 + a2 = -2.598076211 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a2 = -2.598076211 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a2 = -2.598076211 + 1.5 a2 = -2.598076211 + 1.5 Combine like terms: -2.598076211 + 1.5 = -1.098076211 a2 = -1.098076211 Simplifying a2 = -1.098076211 Reorder the terms: 1.098076211 + a2 = -1.098076211 + 1.098076211 Combine like terms: -1.098076211 + 1.098076211 = 0.000000000 1.098076211 + 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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