a^4+1=10

Solution for a^4+1=10 equation:

Simplifying
a4 + 1 = 10

Reorder the terms:
1 + a4 = 10

Solving
1 + a4 = 10

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a4 = 10 + -1

Combine like terms: 1 + -1 = 0
0 + a4 = 10 + -1
a4 = 10 + -1

Combine like terms: 10 + -1 = 9
a4 = 9

Simplifying
a4 = 9

Reorder the terms:
-9 + a4 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + a4 = 0

Factor a difference between two squares.
(3 + a2)(-3 + a2) = 0

Subproblem 1
Set the factor '(3 + a2)' equal to zero and attempt to solve:

Simplifying
3 + a2 = 0

Solving
3 + a2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a2 = 0 + -3
a2 = 0 + -3

Combine like terms: 0 + -3 = -3
a2 = -3

Simplifying
a2 = -3

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 '(-3 + a2)' equal to zero and attempt to solve:

Simplifying
-3 + a2 = 0

Solving
-3 + a2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + a2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + a2 = 0 + 3
a2 = 0 + 3

Combine like terms: 0 + 3 = 3
a2 = 3

Simplifying
a2 = 3

Take the square root of each side:
a = {-1.732050808, 1.732050808}
Solution
a = {-1.732050808, 1.732050808}