81x^4=18x^2-1

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Solution for 81x^4=18x^2-1 equation: 


Simplifying
81x4 = 18x2 + -1

Reorder the terms:
81x4 = -1 + 18x2

Solving
81x4 = -1 + 18x2

Solving for variable 'x'.

Reorder the terms:
1 + -18x2 + 81x4 = -1 + 18x2 + 1 + -18x2

Reorder the terms:
1 + -18x2 + 81x4 = -1 + 1 + 18x2 + -18x2

Combine like terms: -1 + 1 = 0
1 + -18x2 + 81x4 = 0 + 18x2 + -18x2
1 + -18x2 + 81x4 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
1 + -18x2 + 81x4 = 0

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

Factor a difference between two squares.
((1 + 3x)(1 + -3x))(1 + -9x2) = 0

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


Subproblem 1
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 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

Subproblem 4
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, -0.3333333333, 0.3333333333}

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