r^4+r^2-4=0

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Solution for r^4+r^2-4=0 equation: 


Simplifying
r4 + r2 + -4 = 0

Reorder the terms:
-4 + r2 + r4 = 0

Solving
-4 + r2 + r4 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + r2 + 4 + r4 = 0 + 4

Reorder the terms:
-4 + 4 + r2 + r4 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + r2 + r4 = 0 + 4
r2 + r4 = 0 + 4

Combine like terms: 0 + 4 = 4
r2 + r4 = 4

The r term is r2.  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.
r2 + 0.25 + r4 = 4 + 0.25

Reorder the terms:
0.25 + r2 + r4 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + r2 + r4 = 4.25

Factor a perfect square on the left side:
(r2 + 0.5)(r2 + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(r2 + 0.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
r2 + 0.5 = 2.061552813

Simplifying
r2 + 0.5 = 2.061552813

Reorder the terms:
0.5 + r2 = 2.061552813

Solving
0.5 + r2 = 2.061552813

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r2 = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r2 = 2.061552813 + -0.5
r2 = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
r2 = 1.561552813

Simplifying
r2 = 1.561552813

Take the square root of each side:
r = {-1.249621068, 1.249621068}


Subproblem 2
r2 + 0.5 = -2.061552813

Simplifying
r2 + 0.5 = -2.061552813

Reorder the terms:
0.5 + r2 = -2.061552813

Solving
0.5 + r2 = -2.061552813

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r2 = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r2 = -2.061552813 + -0.5
r2 = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
r2 = -2.561552813

Simplifying
r2 = -2.561552813

Reorder the terms:
2.561552813 + r2 = -2.561552813 + 2.561552813

Combine like terms: -2.561552813 + 2.561552813 = 0.000000000
2.561552813 + r2 = 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.

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