a^4=625

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Solution for a^4=625 equation:


Simplifying
a4 = 625

Solving
a4 = 625

Solving for variable 'a'.

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

Simplifying
a4 = 625

Reorder the terms:
-625 + a4 = 625 + -625

Combine like terms: 625 + -625 = 0
-625 + a4 = 0

Factor a difference between two squares.
(25 + a2)(-25 + a2) = 0

Factor a difference between two squares.
(25 + a2)((5 + a)(-5 + a)) = 0

Subproblem 1

Set the factor '(25 + a2)' equal to zero and attempt to solve: Simplifying 25 + a2 = 0 Solving 25 + a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + a2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + a2 = 0 + -25 a2 = 0 + -25 Combine like terms: 0 + -25 = -25 a2 = -25 Simplifying a2 = -25 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 '(5 + a)' equal to zero and attempt to solve: Simplifying 5 + a = 0 Solving 5 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + a = 0 + -5 a = 0 + -5 Combine like terms: 0 + -5 = -5 a = -5 Simplifying a = -5

Subproblem 3

Set the factor '(-5 + a)' equal to zero and attempt to solve: Simplifying -5 + a = 0 Solving -5 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + a = 0 + 5 a = 0 + 5 Combine like terms: 0 + 5 = 5 a = 5 Simplifying a = 5

Solution

a = {-5, 5}

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