r^4-16r^2=-55

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Solution for r^4-16r^2=-55 equation: 


Simplifying
r4 + -16r2 = -55

Reorder the terms:
-16r2 + r4 = -55

Solving
-16r2 + r4 = -55

Solving for variable 'r'.

Reorder the terms:
55 + -16r2 + r4 = -55 + 55

Combine like terms: -55 + 55 = 0
55 + -16r2 + r4 = 0

Factor a trinomial.
(5 + -1r2)(11 + -1r2) = 0


Subproblem 1
Set the factor '(5 + -1r2)' equal to zero and attempt to solve:

Simplifying
5 + -1r2 = 0

Solving
5 + -1r2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r2 = 0 + -5
-1r2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1r2 = -5

Divide each side by '-1'.
r2 = 5

Simplifying
r2 = 5

Take the square root of each side:
r = {-2.236067978, 2.236067978}

Subproblem 2
Set the factor '(11 + -1r2)' equal to zero and attempt to solve:

Simplifying
11 + -1r2 = 0

Solving
11 + -1r2 = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1r2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1r2 = 0 + -11
-1r2 = 0 + -11

Combine like terms: 0 + -11 = -11
-1r2 = -11

Divide each side by '-1'.
r2 = 11

Simplifying
r2 = 11

Take the square root of each side:
r = {-3.31662479, 3.31662479}
Solution
r = {-2.236067978, 2.236067978, -3.31662479, 3.31662479}

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