16x^4-10x^2+1=0

Solution for 16x^4-10x^2+1=0 equation:

Simplifying
16x4 + -10x2 + 1 = 0

Reorder the terms:
1 + -10x2 + 16x4 = 0

Solving
1 + -10x2 + 16x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -8x2)(1 + -2x2) = 0

Subproblem 1
Set the factor '(1 + -8x2)' equal to zero and attempt to solve:

Simplifying
1 + -8x2 = 0

Solving
1 + -8x2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -8x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8x2 = 0 + -1
-8x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-8x2 = -1

Divide each side by '-8'.
x2 = 0.125

Simplifying
x2 = 0.125

Take the square root of each side:
x = {-0.353553391, 0.353553391}
Subproblem 2
Set the factor '(1 + -2x2)' equal to zero and attempt to solve:

Simplifying
1 + -2x2 = 0

Solving
1 + -2x2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x2 = 0 + -1
-2x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2x2 = -1

Divide each side by '-2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}
Solution
x = {-0.353553391, 0.353553391, -0.707106781, 0.707106781}