8=-x^4+9x^2

Solution for 8=-x^4+9x^2 equation:

Simplifying
8 = -1x4 + 9x2

Reorder the terms:
8 = 9x2 + -1x4

Solving
8 = 9x2 + -1x4

Solving for variable 'x'.

Reorder the terms:
8 + -9x2 + x4 = 9x2 + -9x2 + -1x4 + x4

Combine like terms: 9x2 + -9x2 = 0
8 + -9x2 + x4 = 0 + -1x4 + x4
8 + -9x2 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
8 + -9x2 + x4 = 0

Factor a trinomial.
(1 + -1x2)(8 + -1x2) = 0

Factor a difference between two squares.
((1 + x)(1 + -1x))(8 + -1x2) = 0

Subproblem 1
Set the factor '(8 + -1x2)' equal to zero and attempt to solve:

Simplifying
8 + -1x2 = 0

Solving
8 + -1x2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x2 = 0 + -8
-1x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1x2 = -8

Divide each side by '-1'.
x2 = 8

Simplifying
x2 = 8

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

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