4p^8-4=0

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Solution for 4p^8-4=0 equation:


Simplifying
4p8 + -4 = 0

Reorder the terms:
-4 + 4p8 = 0

Solving
-4 + 4p8 = 0

Solving for variable 'p'.

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

Add '4' to each side of the equation.
-4 + 4 + 4p8 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 4p8 = 0 + 4
4p8 = 0 + 4

Combine like terms: 0 + 4 = 4
4p8 = 4

Divide each side by '4'.
p8 = 1

Simplifying
p8 = 1

Reorder the terms:
-1 + p8 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + p8 = 0

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

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

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

Subproblem 1

Set the factor '(1 + p4)' equal to zero and attempt to solve: Simplifying 1 + p4 = 0 Solving 1 + p4 = 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 + p4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + p4 = 0 + -1 p4 = 0 + -1 Combine like terms: 0 + -1 = -1 p4 = -1 Simplifying p4 = -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 + 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 3

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 4

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

Solution

p = {-1, 1}

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