6a^4+12a^2-48=0

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Solution for 6a^4+12a^2-48=0 equation:


Simplifying
6a4 + 12a2 + -48 = 0

Reorder the terms:
-48 + 12a2 + 6a4 = 0

Solving
-48 + 12a2 + 6a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-8 + 2a2 + a4) = 0

Factor a trinomial.
6((-4 + -1a2)(2 + -1a2)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-4 + -1a2)' equal to zero and attempt to solve: Simplifying -4 + -1a2 = 0 Solving -4 + -1a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1a2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1a2 = 0 + 4 -1a2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1a2 = 4 Divide each side by '-1'. a2 = -4 Simplifying a2 = -4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(2 + -1a2)' equal to zero and attempt to solve: Simplifying 2 + -1a2 = 0 Solving 2 + -1a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1a2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a2 = 0 + -2 -1a2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1a2 = -2 Divide each side by '-1'. a2 = 2 Simplifying a2 = 2 Take the square root of each side: a = {-1.414213562, 1.414213562}

Solution

a = {-1.414213562, 1.414213562}

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