5x^4-49x^2+36=0

Solution for 5x^4-49x^2+36=0 equation:

Simplifying
5x4 + -49x2 + 36 = 0

Reorder the terms:
36 + -49x2 + 5x4 = 0

Solving
36 + -49x2 + 5x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -5x2)(9 + -1x2) = 0

Factor a difference between two squares.
(4 + -5x2)((3 + x)(3 + -1x)) = 0

Subproblem 1
Set the factor '(4 + -5x2)' equal to zero and attempt to solve:

Simplifying
4 + -5x2 = 0

Solving
4 + -5x2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x2 = 0 + -4
-5x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5x2 = -4

Divide each side by '-5'.
x2 = 0.8

Simplifying
x2 = 0.8

Take the square root of each side:
x = {-0.894427191, 0.894427191}
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

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

Simplifying
x = 3
Solution
x = {-0.894427191, 0.894427191, -3, 3}