4r^4-5r^2-2=0

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Solution for 4r^4-5r^2-2=0 equation: 


Simplifying
4r4 + -5r2 + -2 = 0

Reorder the terms:
-2 + -5r2 + 4r4 = 0

Solving
-2 + -5r2 + 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'.
-0.5 + -1.25r2 + r4 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1.25r2 + 0.5 + r4 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1.25r2 + r4 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1.25r2 + r4 = 0 + 0.5
-1.25r2 + r4 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1.25r2 + r4 = 0.5

The r term is -1.25r2.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25r2 + 0.390625 + r4 = 0.5 + 0.390625

Reorder the terms:
0.390625 + -1.25r2 + r4 = 0.5 + 0.390625

Combine like terms: 0.5 + 0.390625 = 0.890625
0.390625 + -1.25r2 + r4 = 0.890625

Factor a perfect square on the left side:
(r2 + -0.625)(r2 + -0.625) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(r2 + -0.625) equal to 0.943729304 and -0.943729304.


Subproblem 1
r2 + -0.625 = 0.943729304

Simplifying
r2 + -0.625 = 0.943729304

Reorder the terms:
-0.625 + r2 = 0.943729304

Solving
-0.625 + r2 = 0.943729304

Solving for variable 'r'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + r2 = 0.943729304 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + r2 = 0.943729304 + 0.625
r2 = 0.943729304 + 0.625

Combine like terms: 0.943729304 + 0.625 = 1.568729304
r2 = 1.568729304

Simplifying
r2 = 1.568729304

Take the square root of each side:
r = {-1.252489243, 1.252489243}


Subproblem 2
r2 + -0.625 = -0.943729304

Simplifying
r2 + -0.625 = -0.943729304

Reorder the terms:
-0.625 + r2 = -0.943729304

Solving
-0.625 + r2 = -0.943729304

Solving for variable 'r'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + r2 = -0.943729304 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + r2 = -0.943729304 + 0.625
r2 = -0.943729304 + 0.625

Combine like terms: -0.943729304 + 0.625 = -0.318729304
r2 = -0.318729304

Simplifying
r2 = -0.318729304

Reorder the terms:
0.318729304 + r2 = -0.318729304 + 0.318729304

Combine like terms: -0.318729304 + 0.318729304 = 0.000000000
0.318729304 + 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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