X^8x=e^8x

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Solution for X^8x=e^8x equation:


Simplifying
X8x = e8x

Solving
xX8 = e8x

Solving for variable 'x'.

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

Add '-1e8x' to each side of the equation.
-1e8x + xX8 = e8x + -1e8x

Combine like terms: e8x + -1e8x = 0
-1e8x + xX8 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1e8 + X8) = 0

Factor a difference between two squares.
x((e4 + X4)(-1e4 + X4)) = 0

Factor a difference between two squares.
x((e4 + X4)((e2 + X2)(-1e2 + X2))) = 0

Factor a difference between two squares.
x((e4 + X4)((e2 + X2)((e + X)(-1e + X)))) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(e4 + X4)' equal to zero and attempt to solve: Simplifying e4 + X4 = 0 Reorder the terms: X4 + e4 = 0 Solving X4 + e4 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1X4' to each side of the equation. X4 + -1X4 + e4 = 0 + -1X4 Combine like terms: X4 + -1X4 = 0 0 + e4 = 0 + -1X4 e4 = 0 + -1X4 Remove the zero: e4 = -1X4 Add '-1e4' to each side of the equation. e4 + -1e4 = -1X4 + -1e4 Combine like terms: e4 + -1e4 = 0 0 = -1X4 + -1e4 Simplifying 0 = -1X4 + -1e4 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 '(e2 + X2)' equal to zero and attempt to solve: Simplifying e2 + X2 = 0 Reorder the terms: X2 + e2 = 0 Solving X2 + e2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1X2' to each side of the equation. X2 + -1X2 + e2 = 0 + -1X2 Combine like terms: X2 + -1X2 = 0 0 + e2 = 0 + -1X2 e2 = 0 + -1X2 Remove the zero: e2 = -1X2 Add '-1e2' to each side of the equation. e2 + -1e2 = -1X2 + -1e2 Combine like terms: e2 + -1e2 = 0 0 = -1X2 + -1e2 Simplifying 0 = -1X2 + -1e2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 4

Set the factor '(e + X)' equal to zero and attempt to solve: Simplifying e + X = 0 Reorder the terms: X + e = 0 Solving X + e = 0 Move all terms containing x to the left, all other terms to the right. Add '-1X' to each side of the equation. X + -1X + e = 0 + -1X Combine like terms: X + -1X = 0 0 + e = 0 + -1X e = 0 + -1X Remove the zero: e = -1X Add '-1e' to each side of the equation. e + -1e = -1X + -1e Combine like terms: e + -1e = 0 0 = -1X + -1e Simplifying 0 = -1X + -1e 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 '(-1e + X)' equal to zero and attempt to solve: Simplifying -1e + X = 0 Reorder the terms: X + -1e = 0 Solving X + -1e = 0 Move all terms containing x to the left, all other terms to the right. Add '-1X' to each side of the equation. X + -1X + -1e = 0 + -1X Combine like terms: X + -1X = 0 0 + -1e = 0 + -1X -1e = 0 + -1X Remove the zero: -1e = -1X Add 'e' to each side of the equation. -1e + e = -1X + e Combine like terms: -1e + e = 0 0 = -1X + e Simplifying 0 = -1X + e The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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