9x^8-148x^4+64=0

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Solution for 9x^8-148x^4+64=0 equation: 


Simplifying
9x8 + -148x4 + 64 = 0

Reorder the terms:
64 + -148x4 + 9x8 = 0

Solving
64 + -148x4 + 9x8 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -9x4)(16 + -1x4) = 0

Factor a difference between two squares.
((2 + 3x2)(2 + -3x2))(16 + -1x4) = 0

Factor a difference between two squares.
((4 + x2)(4 + -1x2))(2 + 3x2)(2 + -3x2) = 0

Factor a difference between two squares.
((4 + x2)((2 + x)(2 + -1x)))(2 + 3x2)(2 + -3x2) = 0


Subproblem 1
Set the factor '(2 + 3x2)' equal to zero and attempt to solve:

Simplifying
2 + 3x2 = 0

Solving
2 + 3x2 = 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 + 3x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x2 = 0 + -2
3x2 = 0 + -2

Combine like terms: 0 + -2 = -2
3x2 = -2

Divide each side by '3'.
x2 = -0.6666666667

Simplifying
x2 = -0.6666666667

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 '(2 + -3x2)' equal to zero and attempt to solve:

Simplifying
2 + -3x2 = 0

Solving
2 + -3x2 = 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 + -3x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x2 = 0 + -2
-3x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3x2 = -2

Divide each side by '-3'.
x2 = 0.6666666667

Simplifying
x2 = 0.6666666667

Take the square root of each side:
x = {-0.816496581, 0.816496581}

Subproblem 3
Set the factor '(4 + x2)' equal to zero and attempt to solve:

Simplifying
4 + x2 = 0

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

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

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

Simplifying
x2 = -4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 4
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2

Subproblem 5
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.816496581, 0.816496581, -2, 2}

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