8x^4-7x^2-1=0

Solution for 8x^4-7x^2-1=0 equation:

Simplifying
8x4 + -7x2 + -1 = 0

Reorder the terms:
-1 + -7x2 + 8x4 = 0

Solving
-1 + -7x2 + 8x4 = 0

Solving for variable 'x'.

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

Factor a difference between two squares.
(-1 + -8x2)((1 + x)(1 + -1x)) = 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

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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-1, 1}