10x^4-91x^2+9=0

Solution for 10x^4-91x^2+9=0 equation:

Simplifying
10x4 + -91x2 + 9 = 0

Reorder the terms:
9 + -91x2 + 10x4 = 0

Solving
9 + -91x2 + 10x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -10x2)(9 + -1x2) = 0

Factor a difference between two squares.
(1 + -10x2)((3 + x)(3 + -1x)) = 0

Subproblem 1
Set the factor '(1 + -10x2)' equal to zero and attempt to solve:

Simplifying
1 + -10x2 = 0

Solving
1 + -10x2 = 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 + -10x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -10x2 = 0 + -1
-10x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-10x2 = -1

Divide each side by '-10'.
x2 = 0.1

Simplifying
x2 = 0.1

Take the square root of each side:
x = {-0.316227766, 0.316227766}
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 = {-0.316227766, 0.316227766, -3, 3}