2a^4-8=0

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Solution for 2a^4-8=0 equation:


Simplifying
2a4 + -8 = 0

Reorder the terms:
-8 + 2a4 = 0

Solving
-8 + 2a4 = 0

Solving for variable 'a'.

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

Add '8' to each side of the equation.
-8 + 8 + 2a4 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 2a4 = 0 + 8
2a4 = 0 + 8

Combine like terms: 0 + 8 = 8
2a4 = 8

Divide each side by '2'.
a4 = 4

Simplifying
a4 = 4

Reorder the terms:
-4 + a4 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + a4 = 0

Factor a difference between two squares.
(2 + a2)(-2 + a2) = 0

Subproblem 1

Set the factor '(2 + a2)' equal to zero and attempt to solve: Simplifying 2 + a2 = 0 Solving 2 + a2 = 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 + a2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + a2 = 0 + -2 a2 = 0 + -2 Combine like terms: 0 + -2 = -2 a2 = -2 Simplifying a2 = -2 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 + a2)' equal to zero and attempt to solve: Simplifying -2 + a2 = 0 Solving -2 + a2 = 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 + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + a2 = 0 + 2 a2 = 0 + 2 Combine like terms: 0 + 2 = 2 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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