r^4+8r^2-16=0

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Solution for r^4+8r^2-16=0 equation:


Simplifying
r4 + 8r2 + -16 = 0

Reorder the terms:
-16 + 8r2 + r4 = 0

Solving
-16 + 8r2 + r4 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 8r2 + 16 + r4 = 0 + 16

Reorder the terms:
-16 + 16 + 8r2 + r4 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 8r2 + r4 = 0 + 16
8r2 + r4 = 0 + 16

Combine like terms: 0 + 16 = 16
8r2 + r4 = 16

The r term is 8r2.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8r2 + 16 + r4 = 16 + 16

Reorder the terms:
16 + 8r2 + r4 = 16 + 16

Combine like terms: 16 + 16 = 32
16 + 8r2 + r4 = 32

Factor a perfect square on the left side:
(r2 + 4)(r2 + 4) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(r2 + 4) equal to 5.656854249 and -5.656854249.

Subproblem 1

r2 + 4 = 5.656854249 Simplifying r2 + 4 = 5.656854249 Reorder the terms: 4 + r2 = 5.656854249 Solving 4 + r2 = 5.656854249 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r2 = 5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + r2 = 5.656854249 + -4 r2 = 5.656854249 + -4 Combine like terms: 5.656854249 + -4 = 1.656854249 r2 = 1.656854249 Simplifying r2 = 1.656854249 Take the square root of each side: r = {-1.287188506, 1.287188506}

Subproblem 2

r2 + 4 = -5.656854249 Simplifying r2 + 4 = -5.656854249 Reorder the terms: 4 + r2 = -5.656854249 Solving 4 + r2 = -5.656854249 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r2 = -5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + r2 = -5.656854249 + -4 r2 = -5.656854249 + -4 Combine like terms: -5.656854249 + -4 = -9.656854249 r2 = -9.656854249 Simplifying r2 = -9.656854249 Reorder the terms: 9.656854249 + r2 = -9.656854249 + 9.656854249 Combine like terms: -9.656854249 + 9.656854249 = 0.000000000 9.656854249 + 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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