8x^4-42x^2+34=0

Solution for 8x^4-42x^2+34=0 equation:

Simplifying
8x4 + -42x2 + 34 = 0

Reorder the terms:
34 + -42x2 + 8x4 = 0

Solving
34 + -42x2 + 8x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + -21x2 + 4x4) = 0

Factor a trinomial.
2((1 + -1x2)(17 + -4x2)) = 0

Factor a difference between two squares.
2(((1 + x)(1 + -1x))(17 + -4x2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(17 + -4x2)' equal to zero and attempt to solve:

Simplifying
17 + -4x2 = 0

Solving
17 + -4x2 = 0

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

Add '-17' to each side of the equation.
17 + -17 + -4x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -4x2 = 0 + -17
-4x2 = 0 + -17

Combine like terms: 0 + -17 = -17
-4x2 = -17

Divide each side by '-4'.
x2 = 4.25

Simplifying
x2 = 4.25

Take the square root of each side:
x = {-2.061552813, 2.061552813}
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 = {-2.061552813, 2.061552813, -1, 1}