x^2(36x^2+5)=1

Solution for x^2(36x^2+5)=1 equation:

Simplifying
x2(36x2 + 5) = 1

Reorder the terms:
x2(5 + 36x2) = 1
(5 * x2 + 36x2 * x2) = 1
(5x2 + 36x4) = 1

Solving
5x2 + 36x4 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 5x2 + 36x4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 5x2 + 36x4 = 0

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

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

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

Simplifying
-1 + -4x2 = 0

Solving
-1 + -4x2 = 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 + -4x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x2 = 0 + 1
-4x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4x2 = 1

Divide each side by '-4'.
x2 = -0.25

Simplifying
x2 = -0.25

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

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

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

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

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Subproblem 3
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-0.3333333333, 0.3333333333}