5a^8-13a^4-28=0

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Solution for 5a^8-13a^4-28=0 equation: 


Simplifying
5a8 + -13a4 + -28 = 0

Reorder the terms:
-28 + -13a4 + 5a8 = 0

Solving
-28 + -13a4 + 5a8 = 0

Solving for variable 'a'.

Factor a trinomial.
(-7 + -5a4)(4 + -1a4) = 0

Factor a difference between two squares.
(-7 + -5a4)((2 + a2)(2 + -1a2)) = 0


Subproblem 1
Set the factor '(-7 + -5a4)' equal to zero and attempt to solve:

Simplifying
-7 + -5a4 = 0

Solving
-7 + -5a4 = 0

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

Add '7' to each side of the equation.
-7 + 7 + -5a4 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5a4 = 0 + 7
-5a4 = 0 + 7

Combine like terms: 0 + 7 = 7
-5a4 = 7

Divide each side by '-5'.
a4 = -1.4

Simplifying
a4 = -1.4

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 + 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 3
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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