10x^4+3x^2-4=0

Solution for 10x^4+3x^2-4=0 equation:

Simplifying
10x4 + 3x2 + -4 = 0

Reorder the terms:
-4 + 3x2 + 10x4 = 0

Solving
-4 + 3x2 + 10x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -5x2)(1 + -2x2) = 0

Subproblem 1
Set the factor '(-4 + -5x2)' equal to zero and attempt to solve:

Simplifying
-4 + -5x2 = 0

Solving
-4 + -5x2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + -5x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5x2 = 0 + 4
-5x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-5x2 = 4

Divide each side by '-5'.
x2 = -0.8

Simplifying
x2 = -0.8

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 + -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 = {-0.707106781, 0.707106781}