x^4+x^2=85

Solution for x^4+x^2=85 equation:

Simplifying
x4 + x2 = 85

Reorder the terms:
x2 + x4 = 85

Solving
x2 + x4 = 85

Solving for variable 'x'.

Reorder the terms:
-85 + x2 + x4 = 85 + -85

Combine like terms: 85 + -85 = 0
-85 + x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + x2 + 85 + x4 = 0 + 85

Reorder the terms:
-85 + 85 + x2 + x4 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + x2 + x4 = 0 + 85
x2 + x4 = 0 + 85

Combine like terms: 0 + 85 = 85
x2 + x4 = 85

The x term is x2.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x2 + 0.25 + x4 = 85 + 0.25

Reorder the terms:
0.25 + x2 + x4 = 85 + 0.25

Combine like terms: 85 + 0.25 = 85.25
0.25 + x2 + x4 = 85.25

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = 85.25

Calculate the square root of the right side: 9.233092656

Break this problem into two subproblems by setting 
(x2 + 0.5) equal to 9.233092656 and -9.233092656.

Subproblem 1
x2 + 0.5 = 9.233092656

Simplifying
x2 + 0.5 = 9.233092656

Reorder the terms:
0.5 + x2 = 9.233092656

Solving
0.5 + x2 = 9.233092656

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x2 = 9.233092656 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = 9.233092656 + -0.5
x2 = 9.233092656 + -0.5

Combine like terms: 9.233092656 + -0.5 = 8.733092656
x2 = 8.733092656

Simplifying
x2 = 8.733092656

Take the square root of each side:
x = {-2.955180647, 2.955180647}

Subproblem 2
x2 + 0.5 = -9.233092656

Simplifying
x2 + 0.5 = -9.233092656

Reorder the terms:
0.5 + x2 = -9.233092656

Solving
0.5 + x2 = -9.233092656

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x2 = -9.233092656 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = -9.233092656 + -0.5
x2 = -9.233092656 + -0.5

Combine like terms: -9.233092656 + -0.5 = -9.733092656
x2 = -9.733092656

Simplifying
x2 = -9.733092656

Reorder the terms:
9.733092656 + x2 = -9.733092656 + 9.733092656

Combine like terms: -9.733092656 + 9.733092656 = 0.000000000
9.733092656 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.