9x^4=22x^2-8

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Solution for 9x^4=22x^2-8 equation: 


Simplifying
9x4 = 22x2 + -8

Reorder the terms:
9x4 = -8 + 22x2

Solving
9x4 = -8 + 22x2

Solving for variable 'x'.

Reorder the terms:
8 + -22x2 + 9x4 = -8 + 22x2 + 8 + -22x2

Reorder the terms:
8 + -22x2 + 9x4 = -8 + 8 + 22x2 + -22x2

Combine like terms: -8 + 8 = 0
8 + -22x2 + 9x4 = 0 + 22x2 + -22x2
8 + -22x2 + 9x4 = 22x2 + -22x2

Combine like terms: 22x2 + -22x2 = 0
8 + -22x2 + 9x4 = 0

Factor a trinomial.
(4 + -9x2)(2 + -1x2) = 0

Factor a difference between two squares.
((2 + 3x)(2 + -3x))(2 + -1x2) = 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 '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 3
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-1.414213562, 1.414213562, -0.6666666667, 0.6666666667}

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