x^4-35x^2+96=0

Solution for x^4-35x^2+96=0 equation:

Simplifying
x4 + -35x2 + 96 = 0

Reorder the terms:
96 + -35x2 + x4 = 0

Solving
96 + -35x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x2)(32 + -1x2) = 0

Subproblem 1
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(32 + -1x2)' equal to zero and attempt to solve:

Simplifying
32 + -1x2 = 0

Solving
32 + -1x2 = 0

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

Add '-32' to each side of the equation.
32 + -32 + -1x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -1x2 = 0 + -32
-1x2 = 0 + -32

Combine like terms: 0 + -32 = -32
-1x2 = -32

Divide each side by '-1'.
x2 = 32

Simplifying
x2 = 32

Take the square root of each side:
x = {-5.656854249, 5.656854249}
Solution
x = {-1.732050808, 1.732050808, -5.656854249, 5.656854249}