256a^4-p^4=0

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Solution for 256a^4-p^4=0 equation: 


Simplifying
256a4 + -1p4 = 0

Solving
256a4 + -1p4 = 0

Solving for variable 'a'.

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

Add 'p4' to each side of the equation.
256a4 + -1p4 + p4 = 0 + p4

Combine like terms: -1p4 + p4 = 0
256a4 + 0 = 0 + p4
256a4 = 0 + p4
Remove the zero:
256a4 = p4

Divide each side by '256'.
a4 = 0.00390625p4

Simplifying
a4 = 0.00390625p4

Combine like terms: 0.00390625p4 + -0.00390625p4 = 0.00000000
a4 + -0.00390625p4 = 0.00000000

Factor a difference between two squares.
(a2 + 0.0625p2)(a2 + -0.0625p2) = 0.00000000

Factor a difference between two squares.
(a2 + 0.0625p2)((a + 0.25p)(a + -0.25p)) = 0.00000000


Subproblem 1
Set the factor '(a2 + 0.0625p2)' equal to zero and attempt to solve:

Simplifying
a2 + 0.0625p2 = 0

Solving
a2 + 0.0625p2 = 0

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

Add '-0.0625p2' to each side of the equation.
a2 + 0.0625p2 + -0.0625p2 = 0 + -0.0625p2

Combine like terms: 0.0625p2 + -0.0625p2 = 0.0000
a2 + 0.0000 = 0 + -0.0625p2
a2 = 0 + -0.0625p2
Remove the zero:
a2 = -0.0625p2

Simplifying
a2 = -0.0625p2

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 '(a + 0.25p)' equal to zero and attempt to solve:

Simplifying
a + 0.25p = 0

Solving
a + 0.25p = 0

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

Add '-0.25p' to each side of the equation.
a + 0.25p + -0.25p = 0 + -0.25p

Combine like terms: 0.25p + -0.25p = 0.00
a + 0.00 = 0 + -0.25p
a = 0 + -0.25p
Remove the zero:
a = -0.25p

Simplifying
a = -0.25p

Subproblem 3
Set the factor '(a + -0.25p)' equal to zero and attempt to solve:

Simplifying
a + -0.25p = 0

Solving
a + -0.25p = 0

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

Add '0.25p' to each side of the equation.
a + -0.25p + 0.25p = 0 + 0.25p

Combine like terms: -0.25p + 0.25p = 0.00
a + 0.00 = 0 + 0.25p
a = 0 + 0.25p
Remove the zero:
a = 0.25p

Simplifying
a = 0.25p
Solution
a = {-0.25p, 0.25p}

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