z^4-22z^2+121=

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Solution for z^4-22z^2+121= equation: 


Simplifying
z4 + -22z2 + 121 = 0

Reorder the terms:
121 + -22z2 + z4 = 0

Solving
121 + -22z2 + z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(11 + -1z2)(11 + -1z2) = 0


Subproblem 1
Set the factor '(11 + -1z2)' equal to zero and attempt to solve:

Simplifying
11 + -1z2 = 0

Solving
11 + -1z2 = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1z2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1z2 = 0 + -11
-1z2 = 0 + -11

Combine like terms: 0 + -11 = -11
-1z2 = -11

Divide each side by '-1'.
z2 = 11

Simplifying
z2 = 11

Take the square root of each side:
z = {-3.31662479, 3.31662479}

Subproblem 2
Set the factor '(11 + -1z2)' equal to zero and attempt to solve:

Simplifying
11 + -1z2 = 0

Solving
11 + -1z2 = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1z2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1z2 = 0 + -11
-1z2 = 0 + -11

Combine like terms: 0 + -11 = -11
-1z2 = -11

Divide each side by '-1'.
z2 = 11

Simplifying
z2 = 11

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

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