0=x^4+16x^2-36

Solution for 0=x^4+16x^2-36 equation:

Simplifying
0 = x4 + 16x2 + -36

Reorder the terms:
0 = -36 + 16x2 + x4

Solving
0 = -36 + 16x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 36 = 36
36 + -16x2 + -1x4 = -36 + 16x2 + x4 + 36 + -16x2 + -1x4

Reorder the terms:
36 + -16x2 + -1x4 = -36 + 36 + 16x2 + -16x2 + x4 + -1x4

Combine like terms: -36 + 36 = 0
36 + -16x2 + -1x4 = 0 + 16x2 + -16x2 + x4 + -1x4
36 + -16x2 + -1x4 = 16x2 + -16x2 + x4 + -1x4

Combine like terms: 16x2 + -16x2 = 0
36 + -16x2 + -1x4 = 0 + x4 + -1x4
36 + -16x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
36 + -16x2 + -1x4 = 0

Factor a trinomial.
(2 + -1x2)(18 + x2) = 0

Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(18 + x2)' equal to zero and attempt to solve:

Simplifying
18 + x2 = 0

Solving
18 + x2 = 0

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

Add '-18' to each side of the equation.
18 + -18 + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + x2 = 0 + -18
x2 = 0 + -18

Combine like terms: 0 + -18 = -18
x2 = -18

Simplifying
x2 = -18

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-1.414213562, 1.414213562}