X^4-1=15

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Solution for X^4-1=15 equation:


Simplifying
X4 + -1 = 15

Reorder the terms:
-1 + X4 = 15

Solving
-1 + X4 = 15

Solving for variable 'X'.

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

Add '1' to each side of the equation.
-1 + 1 + X4 = 15 + 1

Combine like terms: -1 + 1 = 0
0 + X4 = 15 + 1
X4 = 15 + 1

Combine like terms: 15 + 1 = 16
X4 = 16

Simplifying
X4 = 16

Reorder the terms:
-16 + X4 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + X4 = 0

Factor a difference between two squares.
(4 + X2)(-4 + X2) = 0

Factor a difference between two squares.
(4 + X2)((2 + X)(-2 + X)) = 0

Subproblem 1

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 2

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 3

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

Solution

X = {-2, 2}

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