5x^4+13x^2-8=x^2+1

Solution for 5x^4+13x^2-8=x^2+1 equation:

Simplifying
5x4 + 13x2 + -8 = x2 + 1

Reorder the terms:
-8 + 13x2 + 5x4 = x2 + 1

Reorder the terms:
-8 + 13x2 + 5x4 = 1 + x2

Solving
-8 + 13x2 + 5x4 = 1 + x2

Solving for variable 'x'.

Reorder the terms:
-8 + -1 + 13x2 + -1x2 + 5x4 = 1 + x2 + -1 + -1x2

Combine like terms: -8 + -1 = -9
-9 + 13x2 + -1x2 + 5x4 = 1 + x2 + -1 + -1x2

Combine like terms: 13x2 + -1x2 = 12x2
-9 + 12x2 + 5x4 = 1 + x2 + -1 + -1x2

Reorder the terms:
-9 + 12x2 + 5x4 = 1 + -1 + x2 + -1x2

Combine like terms: 1 + -1 = 0
-9 + 12x2 + 5x4 = 0 + x2 + -1x2
-9 + 12x2 + 5x4 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-9 + 12x2 + 5x4 = 0

Factor a trinomial.
(-3 + -1x2)(3 + -5x2) = 0

Subproblem 1
Set the factor '(-3 + -1x2)' equal to zero and attempt to solve:

Simplifying
-3 + -1x2 = 0

Solving
-3 + -1x2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x2 = 0 + 3
-1x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1x2 = 3

Divide each side by '-1'.
x2 = -3

Simplifying
x2 = -3

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 '(3 + -5x2)' equal to zero and attempt to solve:

Simplifying
3 + -5x2 = 0

Solving
3 + -5x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x2 = 0 + -3
-5x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-5x2 = -3

Divide each side by '-5'.
x2 = 0.6

Simplifying
x2 = 0.6

Take the square root of each side:
x = {-0.774596669, 0.774596669}
Solution
x = {-0.774596669, 0.774596669}