4r^4-r^2-12=0

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Solution for 4r^4-r^2-12=0 equation: 


Simplifying
4r4 + -1r2 + -12 = 0

Reorder the terms:
-12 + -1r2 + 4r4 = 0

Solving
-12 + -1r2 + 4r4 = 0

Solving for variable 'r'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-3 + -0.25r2 + r4 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -0.25r2 + 3 + r4 = 0 + 3

Reorder the terms:
-3 + 3 + -0.25r2 + r4 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -0.25r2 + r4 = 0 + 3
-0.25r2 + r4 = 0 + 3

Combine like terms: 0 + 3 = 3
-0.25r2 + r4 = 3

The r term is -0.25r2.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25r2 + 0.015625 + r4 = 3 + 0.015625

Reorder the terms:
0.015625 + -0.25r2 + r4 = 3 + 0.015625

Combine like terms: 3 + 0.015625 = 3.015625
0.015625 + -0.25r2 + r4 = 3.015625

Factor a perfect square on the left side:
(r2 + -0.125)(r2 + -0.125) = 3.015625

Calculate the square root of the right side: 1.736555499

Break this problem into two subproblems by setting 
(r2 + -0.125) equal to 1.736555499 and -1.736555499.


Subproblem 1
r2 + -0.125 = 1.736555499

Simplifying
r2 + -0.125 = 1.736555499

Reorder the terms:
-0.125 + r2 = 1.736555499

Solving
-0.125 + r2 = 1.736555499

Solving for variable 'r'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + r2 = 1.736555499 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + r2 = 1.736555499 + 0.125
r2 = 1.736555499 + 0.125

Combine like terms: 1.736555499 + 0.125 = 1.861555499
r2 = 1.861555499

Simplifying
r2 = 1.861555499

Take the square root of each side:
r = {-1.364388324, 1.364388324}


Subproblem 2
r2 + -0.125 = -1.736555499

Simplifying
r2 + -0.125 = -1.736555499

Reorder the terms:
-0.125 + r2 = -1.736555499

Solving
-0.125 + r2 = -1.736555499

Solving for variable 'r'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + r2 = -1.736555499 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + r2 = -1.736555499 + 0.125
r2 = -1.736555499 + 0.125

Combine like terms: -1.736555499 + 0.125 = -1.611555499
r2 = -1.611555499

Simplifying
r2 = -1.611555499

Reorder the terms:
1.611555499 + r2 = -1.611555499 + 1.611555499

Combine like terms: -1.611555499 + 1.611555499 = 0.000000000
1.611555499 + 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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