p^8-10p^4+9=0

Solution for p^8-10p^4+9=0 equation:

Simplifying
p8 + -10p4 + 9 = 0

Reorder the terms:
9 + -10p4 + p8 = 0

Solving
9 + -10p4 + p8 = 0

Solving for variable 'p'.

Factor a trinomial.
(1 + -1p4)(9 + -1p4) = 0

Factor a difference between two squares.
((1 + p2)(1 + -1p2))(9 + -1p4) = 0

Factor a difference between two squares.
((1 + p2)((1 + p)(1 + -1p)))(9 + -1p4) = 0

Factor a difference between two squares.
((3 + p2)(3 + -1p2))(1 + p2)(1 + p)(1 + -1p) = 0

Subproblem 1
Set the factor '(1 + p2)' equal to zero and attempt to solve:

Simplifying
1 + p2 = 0

Solving
1 + p2 = 0

Move all terms containing p to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + p2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + p2 = 0 + -1
p2 = 0 + -1

Combine like terms: 0 + -1 = -1
p2 = -1

Simplifying
p2 = -1

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 + p)' equal to zero and attempt to solve:

Simplifying
1 + p = 0

Solving
1 + p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + p = 0 + -1
p = 0 + -1

Combine like terms: 0 + -1 = -1
p = -1

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

Simplifying
1 + -1p = 0

Solving
1 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1p = 0 + -1
-1p = 0 + -1

Combine like terms: 0 + -1 = -1
-1p = -1

Divide each side by '-1'.
p = 1

Simplifying
p = 1
Subproblem 4
Set the factor '(3 + p2)' equal to zero and attempt to solve:

Simplifying
3 + p2 = 0

Solving
3 + p2 = 0

Move all terms containing p to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + p2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + p2 = 0 + -3
p2 = 0 + -3

Combine like terms: 0 + -3 = -3
p2 = -3

Simplifying
p2 = -3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 5
Set the factor '(3 + -1p2)' equal to zero and attempt to solve:

Simplifying
3 + -1p2 = 0

Solving
3 + -1p2 = 0

Move all terms containing p to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1p2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p2 = 0 + -3
-1p2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1p2 = -3

Divide each side by '-1'.
p2 = 3

Simplifying
p2 = 3

Take the square root of each side:
p = {-1.732050808, 1.732050808}
Solution
p = {-1, 1, -1.732050808, 1.732050808}