c^4-9c^2=-8

Solution for c^4-9c^2=-8 equation:

Simplifying
c4 + -9c2 = -8

Reorder the terms:
-9c2 + c4 = -8

Solving
-9c2 + c4 = -8

Solving for variable 'c'.

Reorder the terms:
8 + -9c2 + c4 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + -9c2 + c4 = 0

Factor a trinomial.
(1 + -1c2)(8 + -1c2) = 0

Factor a difference between two squares.
((1 + c)(1 + -1c))(8 + -1c2) = 0

Subproblem 1
Set the factor '(8 + -1c2)' equal to zero and attempt to solve:

Simplifying
8 + -1c2 = 0

Solving
8 + -1c2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1c2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1c2 = 0 + -8
-1c2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1c2 = -8

Divide each side by '-1'.
c2 = 8

Simplifying
c2 = 8

Take the square root of each side:
c = {-2.828427125, 2.828427125}
Subproblem 2
Set the factor '(1 + c)' equal to zero and attempt to solve:

Simplifying
1 + c = 0

Solving
1 + c = 0

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

Add '-1' to each side of the equation.
1 + -1 + c = 0 + -1

Combine like terms: 1 + -1 = 0
0 + c = 0 + -1
c = 0 + -1

Combine like terms: 0 + -1 = -1
c = -1

Simplifying
c = -1
Subproblem 3
Set the factor '(1 + -1c)' equal to zero and attempt to solve:

Simplifying
1 + -1c = 0

Solving
1 + -1c = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1c = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1c = 0 + -1
-1c = 0 + -1

Combine like terms: 0 + -1 = -1
-1c = -1

Divide each side by '-1'.
c = 1

Simplifying
c = 1
Solution
c = {-2.828427125, 2.828427125, -1, 1}