v^4-10v^2+16=0

Solution for v^4-10v^2+16=0 equation:

Simplifying
v4 + -10v2 + 16 = 0

Reorder the terms:
16 + -10v2 + v4 = 0

Solving
16 + -10v2 + v4 = 0

Solving for variable 'v'.

Factor a trinomial.
(2 + -1v2)(8 + -1v2) = 0

Subproblem 1
Set the factor '(2 + -1v2)' equal to zero and attempt to solve:

Simplifying
2 + -1v2 = 0

Solving
2 + -1v2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1v2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1v2 = 0 + -2
-1v2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1v2 = -2

Divide each side by '-1'.
v2 = 2

Simplifying
v2 = 2

Take the square root of each side:
v = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(8 + -1v2)' equal to zero and attempt to solve:

Simplifying
8 + -1v2 = 0

Solving
8 + -1v2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1v2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1v2 = 0 + -8
-1v2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1v2 = -8

Divide each side by '-1'.
v2 = 8

Simplifying
v2 = 8

Take the square root of each side:
v = {-2.828427125, 2.828427125}
Solution
v = {-1.414213562, 1.414213562, -2.828427125, 2.828427125}